Students practice finding the constant k from tables and graphs using the formula k = y/x (Activity 2 and Activity 3). Students rewrite and solve equations in the form y = kx and use those equations to solve contextual problems (Activity 5 and Activity 6, e.g., y = 60x and y = 4x). Students select points on graphs and compute k as a rate (distance/time, dollars/hour) and identify proportional graphs as lines that pass through the origin.

Students repeatedly write and use equations of the form y = kx (e.g., Jim's earnings y = 12x, examples y = 4x, y = 5x, y = 8x) and build tables and graphs from those equations. Students identify and interpret the unit rate k as the slope by locating the point (1, k) and by describing how much y increases for each 1-unit increase in x (many activities ask for the unit rate and label points like (1,10) or (1,65)). Students compare slopes in context (steepness to determine fastest or best rate) in examples such as cyclists, pool filling rates, and pizza costs, using the equation to generate points and interpret the meaning of the rate.

Students write and use linear equations in proportional form (y = kx / t = p·n) in multiple activities (e.g., t = 12n for movie tickets, t = 15n for pizzas, a = r h for painting). Students solve those equations for unknowns in context (e.g., 156 = 10m solved to find m = 15.6 minutes burned, 100 = 20h solved to find h = 5). Students identify and compute the unit rate/constant of proportionality from tables and graphs and interpret a point like (1, 5) as the unit rate; they are also asked to determine if relationships are proportional by checking for a constant rate and a line through the origin.

Students set up and solve linear equations that relate two quantities (for example, 0.012 × V = $2,400 to find property value and 1.08 × x = $212 to find pre-tax price). Students compute commission and total earnings using formulas of the form Commission = Sales × Rate and Total Earnings = Base Salary + Commission, and they solve forward and backward problems that use these equations. Students also calculate total price from Original Price and Tax using Total = (1 + rate) × Original Price in multiple practice problems.

Students use the linear formula I = Prt repeatedly: they calculate interest earned (I) given principal, rate, and time and solve for missing values such as rate or time on multiple activity pages and worked examples. Activity problems require rearranging I = Prt to find r or t (e.g., 250 = 2500 × r × 2 → r = 5%, and 108 = 600 × 0.06 × t → t = 3 years). Students compute balances using Balance = Principal + Interest, showing they apply a linear relationship between time (or principal) and interest in financial contexts.

Students repeatedly compute unit rates from contextual scenarios (e.g., miles per hour, price per item, earnings per hour) and write equations of proportional relationships in the form y = kx (several problems ask for y = (3/5)x, y = (2/7)x, y = 4x, etc.). Students plot and analyze graphs that are straight lines through the origin (e.g., Hours Worked vs. Money Earned) and identify the meaning of points such as (0,0) and (1,r). Several tasks ask students to find the constant of proportionality from tables and use those equations to solve word problems about costs, rates, and unit conversions.

Students create tables and plot number-of-lemons vs. total-cost lines for different stores and answer which line is steepest, with guidance that steepness corresponds to price per lemon. Students write equations of the form y = kx for the recipe scaling tasks (e.g., y = 2x for tablespoons of lemon juice and y = 1.5x for tablespoons of sugar) and use those equations to compute amounts for up to 16 cups. Students set up proportions and arithmetic equations to compute total cost for one gallon and to find cost per cup using the unit prices they calculated.

Students write and use linear equations in context, for example Total Cost = 25 + 3r for fair costs and Selling Price = Wholesale Price + (Wholesale Price × Markup Rate) which is rewritten as Selling Price = Wholesale Price × (1 + Markup Rate). Students solve those equations for unknowns (e.g., compute total cost for 5 rides or solve 25 + 3r = 58 to find r = 11). Activities require setting up the equation from a context and using algebraic steps to solve for original price, total price, or number of items.

Students set up and solve linear equations in context, for example writing and solving t = cp + s (markers problem) and s = r(m + t) (rides problem) as well as using P = 2(l + w) to find missing rectangle sides. Students define variables for real situations (cost per pack, shipping fee, number of packs; cost per ride, number of rides) and carry out algebraic steps (subtracting the fixed term, dividing by the coefficient) to solve for the unknown. Multiple activity pages require students to solve equations of the form ax + b = c and a(x + b) = c in contextual word problems.

Students compute the unit rate (k) from graphs and points and write equations in the form y = kx (e.g., earnings $10/hr, walking 2 miles/hr, apples $3/lb). Students plot points from equations (Activity 3), generate tables of x and y, and use the equation y = kx to find or predict y-values for given x-values. Activities explicitly ask students to turn graphs into equations by dividing y by x and to identify the unit rate as the slope.

Students write and use linear equations of the form y = mx (e.g., y = 4x, y = 3x, y = 60x) to model bivariate measurement situations (distance/time, money saved, paint pigment per liter). Students calculate slope from two points using m = (y2 - y1)/(x2 - x1) in tables and graphs and then interpret that slope as a unit rate in context (miles per hour, dollars per week, ml per liter). Students graph equations and compare which line is steeper to determine which situation has the greater rate of change.

Students calculate x- and y-intercepts algebraically by setting y = 0 and x = 0 in provided linear equations (examples include 2x + 4y = 8, 3x - 6y = 12, y = 5x + 10) and solving for the remaining variable. Students identify intercepts from graphs and plot lines using given intercept pairs (activities ask them to write ordered pairs like (3,0) and (0,-2) and graph lines from intercepts such as (2,0) and (0,4)). The parent plan and skills list explicitly mention deriving y = mx and y = mx + b and interpreting y = mx + b as defining a linear function, linking equation form to intercepts.

Students translate context and data into y = mx + b in multiple places: Activity 8 has students write and graph y = 10x + 50 for Liam's pay and identify the slope as $10/hour and the intercept as the $50 bonus. Activity 7 has students find slopes from tables (m = change in y / change in x), solve for b, write the equation, and graph the resulting model. Activity 6 has students compute slope from two points, substitute into y = mx + b to solve for b, and then use the equation to plot and extend the line.

Students translate contextual bivariate data (hours vs. earnings, days vs. cost) into linear equations by identifying slope and y-intercept from tables and graphs (e.g., babysitting, car rental, dog walker, lawn care problems). Students write equations in slope-intercept form (y = mx + b) and explicitly identify slope and intercept in context (e.g., "You're earning $12/hour plus a $20 bonus" → y = 12x + 20; slope = 12, y-intercept = 20). Students use those equations to solve contextual problems (e.g., 30 + 10x = 80 → x = 5 GB; 24 + 3x = 66 → x = 14 rides) and are asked to explain the meaning of the y-intercept in at least one scenario.

Students write and use linear equations y = mx to model distance vs. time for car, train, and plane (e.g., y = 60x, y = 80x, y = 400x) and solve those equations to find travel time for a 500-mile trip (500 = 60x, etc.). Students graph the same linear models, compute rise/run for a line, and answer which mode is fastest/slowest based on slope, showing interpretation of slope as a unit rate (speed). Students also write and use cost models in the form y = mx + b, identify the slope (cost per mile) and intercept (fixed starting cost), and solve equations set equal to find a break-even distance (0.15x + 31.50 = 0.20x + 20.75 → x = 215).

Students write and use linear equations such as y = 2x + 1, y = 3x − 4, and y = −2x + 3 to compute outputs from given inputs and complete input/output tables. Students plot those input/output pairs on coordinate grids and connect them to form straight lines, explicitly noting that the line crosses the y-axis at a specific value. Students are told and shown that linear functions change at a constant rate and given examples where they observe that increasing x by 1 increases y by a fixed amount (e.g., y increases by 2 for y = 2x + 1).

Students plug x-values into linear equations (e.g., y = 2x + 4) to compute y and complete tables, and they plot those points on coordinate planes. The lesson explicitly labels the y-intercept (0, 4) and the slope (2) and describes the slope as a rise of 2 units for every 1 unit of run. Students also examine contextual examples (walking the dog: 100 steps per minute) and compare graphs and tables to determine constant rate of change.

Students compute and plot positions from given rates and times in the Sloth, Turtle, and Balloon activities (e.g., climb at 4 ft/hr for 3 hours, then 5 ft/hr for 2 hours), marking points and connecting them to make linear segments. Several graphs (Graph B, the money-earned example, and other linear upward/downward graphs) present constant-rate (linear) relationships with labeled axes, so students match scenarios to straight-line graphs and reason about constant rates. The parent plan and activity descriptions explicitly say students "calculate positions over time" and practice translating a narrative rate into plotted points.

Students set x = 0 and y = 0 to find y- and x-intercepts from equations such as 2y + 3x = 4 and y = 2x + 3, showing step-by-step algebraic solutions. Students identify intercepts from graphs and tables by locating where a line crosses the axes or where rows show x = 0 or y = 0 and record answers as coordinate pairs on activity pages. Students interpret intercepts in context in word problems (e.g., a $50 prepaid card: y-intercept = (0, 50); walking/water problem: y-intercept = starting ounces, x-intercept = miles when water is 0).

Students calculate slope from graphs, ordered pairs, and tables using the formula m = (y2 − y1)/(x2 − x1). Students identify slope and y-intercept from equations by rewriting equations into y = mx + b and extracting m and b. Students practice labeling rise, run, and slope on multiple activity pages and complete examples that compute numeric slope values.

Students work with contextual examples (Ellie's subway trips) where they identify two points, compute slope and y-intercept, and write the linear equation y = 2x + 2 from the graph. The Table to Equation activity gives x (minutes) and y (miles), has students compute m = 1/5 miles per minute, converts that rate to 12 miles per hour, finds b = 0, and writes the model y = (1/5)x. Multiple activities require students to find slope and y-intercept from tables, graphs, or points and then write and use the equation y = mx + b to graph or evaluate the relationship.

Students write linear equations from real-world descriptions (e.g., Liam: A = 6c + 12; Sasha: T = 10n + 20) and from tables and graphs (e.g., P = 15h from a reading table; C = 3h + 5 from a rental-cost graph). Students identify the slope as the rate of change (e.g., "$6 per chore", "15 pages per hour", "$3 per hour") and the y-intercept as the starting value or flat fee (e.g., $12 saved, 0 pages at 0 hours, $5 flat fee). Activities ask students to name input and output variables, compute slope using the slope formula from two points, and write function rules in the form output = slope × input + starting value.

Students read and interpret linear equations in context (e.g., Jordan's y = -3x + 100 where students identify slope = -3 and y-intercept = 100 and interpret these as losing $3 per week and starting with $100). Multiple student activities present equations (H = 4x + 10, y = -10x + 50, d = 3t + 2, d = t + 4) and ask students to compare rates of change and starting values between an equation and another representation. Answer keys and worked examples show students computing slopes from equations and using the y-intercept as the starting value in context (for instance, comparing who started closer to a location or who is losing money faster).

Students write linear equations for real contexts (e.g., E = 12h, Liam: y = 2x + 17, gym membership y = 15x + 25) and construct slope-intercept equations (e.g., write y = 3x - 1, y = 4x - 3). Students find rates of change from bivariate tables (train distance/time → 60 miles per hour) and identify y- and x-intercepts from equations and graphs. Students interpret slope and intercept in context through tasks such as comparing starting fees and rates of increase for streaming services and explaining the meaning of a slope of 0.

Students are asked to write equations and identify slope and y-intercepts in multiple places: Blue card examples include questions like "What is the slope and y-intercept of y = -2x + 5?" and matching equations to real-world stories (e.g., $20 start and $15 per hour). Yellow card examples ask students to write an equation from a scenario (Emma earns $10 per hour) and compute outcomes (earnings for 5 hours; temperature after 4 hours given a rate of change). Green cards require students to read tables of (x,y) pairs and "Write an equation for the table" or "Identify the slope from a table." The Parent Plan repeatedly directs students to determine and interpret rate of change and initial value from descriptions, tables, or graphs.

Students set up and solve linear equations from real-world contexts (e.g., 50 + 8.75g = 312.50 for catering costs; 85h + 200 = 965 for contractor payment; 4(y+2)=16 for cupcakes) and solve for the unknown using multi-step algebra. Several problems label parts of the equation in context (e.g., y = cupcakes each person baked, +2 = Grandma's gift, 4 = number of bakers) and students practice forming an equation from a described relationship then solving it.

Students repeatedly set up and solve linear equations that model two-variable contexts (e.g., 25 + 15x = 130 for a gym sign-up and monthly fee; 18x + 20 = 146 for a subscription; 40 + 0.30x = 94 for van rental; 25 + 7x = 10 + 8x for comparing phone plans). Directions ask students to identify key details (sign-up fee, monthly charge), define a variable, translate the scenario into an equation, and solve for the unknown. Several worked examples show substitution of the solution back into the context to verify the answer.

Students practice rewriting equations into slope-intercept form and identifying m (slope) and b (y-intercept) (Activity 6 and Day 2). Students graph equations in y = mx + b form, use rise/run to plot points, and verify intersection points by substituting coordinate pairs into equations (Activity 1, Activity 3). Students compare slopes and intercepts to decide whether systems have one, none, or infinitely many solutions without graphing, showing attention to the roles of slope and intercept in line behavior (Activity 6).

Students practice finding the equation of a line in slope–intercept form from two given points in multiple activities and examples. Students solve contextual word problems that use linear relationships (delivery flat fee + per-mile fee, babysitting flat fee + hourly rate) by setting up and solving linear equations. Students use those equations to solve for unknowns and apply substitution and elimination to find intersection points of linear relationships.

Students write linear equations in slope-intercept form (y = mx + b) for contextual situations (e.g., y = 20x + 50 and y = 30x for cleaning companies; y = 2x + 15 and y = 5x for streaming services). Students solve those linear models to find break-even points by solving systems (e.g., 30x = 20x + 50 leads to x = 5, y = 150). Students use the models to make decisions about which option is cheaper for ranges of x (fewer or more hours/movies) and note that the fixed fee corresponds to a flat cost while the rate corresponds to a per-unit charge.

Students solve contextual one-variable linear equations that come from linear models (e.g., 12h + 50 = 122, 25 + 5c = 60, lemonade and ticket price problems) and use those equations to find unknowns. Students calculate slope and y-intercept from lines given by equations or two points (problems asking for slope through points, graph y = 2x - 1, and identifying y-intercepts). Students solve systems by graphing and interpret the point of intersection as the solution to a system (several graphing/system problems and answer key identify intersection points).

Students write linear equations for real-world bivariate situations (e.g., Housing: C = 1200m and C = 1500 + 1050m; Transportation: C = 225 + 0.60x and C = 1.25x; Entertainment: C = 20 and C = 5 + 1.5h; Meal Plans and Phone Plans similarly). Students graph those equations, find intersections/break-even points algebraically (setting equations equal and solving by substitution or elimination), and use graphs to confirm solutions. Students are asked to identify y-intercepts and slopes from graphs (Meal Plans) and to interpret what those values mean in context (e.g., furniture as a one-time cost, per-week or per-mile cost, how roommate splitting changes per-person cost).

Students practice identifying linear trends and drawing or choosing best-fit lines on scatterplots (Activity 3: Best Fit Line; Part 3: Draw Your Own Best Fit Line). Students use those lines to make numeric predictions from bivariate data, including predicting values within the data range and extrapolating beyond it (Making Predictions example: predict recital score for 3 and 8 hours). Students identify independent and dependent variables and place them on axes in multiple activities, so they work with contextual bivariate measurement data.

Students repeatedly plot bivariate data and are instructed to "Draw a best fit line (if needed)" and to "Interpret the graph," answering prediction questions such as expected values at unobserved x (e.g., predict grade for 8 hours, predict problems solved for 5 hours, predict arm span for 74 in). One example text explicitly notes an approximate rate of change ("Each additional hour studied corresponds to approximately a 10% increase in test grade"), and multiple activities ask students to describe whether the relationship is linear and to use the trend to make numeric predictions.

Students practice creating linear models by writing equations for lines of best fit from scatterplots (Activity 1 and multiple student pages). They identify independent and dependent variables, compute slope and y-intercept from two points, and match or write y = mx + b equations (example problems and answer key). Students interpret slope and intercept in words and use the equation to make predictions and solve contextual problems (the ice cream example predicting sales at 70°F and numerous problem pages asking for predictions).

The Parent Plan Skills list explicitly states that students should "Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept," and even gives an example interpreting a slope. Several student activities ask students to match or write linear equations for scatterplots (Question 13: choose between given equations; Question 14: write an equation for a scatterplot). Multiple tasks ask students to make numerical predictions from scatterplots (predict mood at 12 hours, predict homework at 8 hours, estimate texts at 9 hours), which requires using a linear fit or model to solve contextual problems.

Students write and graph linear equations such as y = 6x, y = 4x, and y = x + 6 and match tables to those equations. Students identify and use the constant of proportionality as the slope (e.g., k = 5, k = 4) and answer questions about what points like (0,0) and (1,6) represent in context. Students solve contextual problems using these equations (e.g., y = 15x for monthly cost) and read totals from graphs for given x-values.

Students write linear equations from tables and graphs and use them to compute contextual values (Activity 2 babysitting and car rental tasks ask students to write y = kx and interpret (0,0); Activity 4 phone plans asks students to graph y = 20x and y = 15x + 30 and determine which plan costs more after 4 months). Activity 3 explicitly asks students to write an equation for a delivery service (y = 18x + 12), identify slope and y-intercept, and explain what each represents. Several tasks require finding slope from two points, writing y = mx + b, and interpreting slope as a unit rate and intercept as a starting value in context.

Students write equations from contextual bivariate situations (e.g., problem 34: runner travels 6 miles in 1.5 hours — find unit rate and equation; problem 33: movie tickets cost $11 each plus a $4 fee — write C = 11t + 4 and compute cost). Students graph given linear equations and describe relationships (problem 20: graph y = 4x and the answer interprets the slope as "for every 1 unit increase in x, y increases by 4" and notes the line passes through the origin). Students identify slope and intercept from equations and plotted lines (problems 35–37 and problem 36 asking for slope and intercept of y = 3x + 8).

Students write linear equations from real-world contexts (e.g., y = 18h for earnings, y = 12x + 10 for bike rental) and identify the slope and y-intercept in those equations. Students compute slopes from two points and from equations (e.g., slope from (2,1) and (6,9); slope = −1.25 from y = −1.25x + 5) and explain the meaning of slope as a rate of change. Students find x- and y-intercepts from tables, graphs, and standard-form equations and explain what those intercepts represent in context (taxi starting cost, where total cost is zero, value at x = 0).

Students calculate slope from two given points and graph lines in slope-intercept form (Activity 2 asks for slope from points and to graph y = x - 3 and y = -2x + 1). Students translate real-life situations into linear equations, define variables, solve those equations, and state contextual answers (Activity 4 has gym, taxi, streaming, and ticket problems where students write equations like 25 + 15m = 100 and solve for m). Students solve and interpret solution values in context (Activity 4 answer keys give contextual solutions such as 5 months or 14 miles).

Activity 3 asks students to analyze scatterplots, identify types of correlation, interpret relationships, and consider what lines of best fit show (e.g., "What does this relationship suggest?" and "What does it mean if most data points are close to the line of best fit?"). A web resource titled "Write an Equation for a Line of Best Fit" is listed alongside the scatterplot activities. The Parent Plan skill list explicitly names "Use the equation of a linear model to solve problems… interpreting the slope and intercept."

Students write and use linear equations in context (Problem 8: "You earn $10 per hour. Write a function..." with answer y = 10x) and solve contextual linear problems (Problem 35: tutor charges $18/hour plus $30 fee; students solve for hours). Students calculate slope and intercept from equations and points (Problem 3: find y-intercept of y = 3x + 4; Problem 4: find x-intercept from a table; Problem 5: find slope through two points). Students also analyze bivariate data visuals by identifying correlation and discussing the line of best fit (Problems 46 and 47).