Students work with graphs of proportional relationships and are asked to interpret straight lines as models of two quantities (e.g., car distance vs. time, constant speed producing a straight line through the origin). In Activity 3 students pick points on a plotted line and compute k = y/x, and Activity 5 has them rewrite equations in y = kx form so they can interpret the slope as a constant rate. The optional data-collection activity has students gather paired measurements, build a table, find k, write y = kx, and use the equation to make predictions.

Students repeatedly plot pairs of quantitative values and draw straight lines through the points (Activities 1, 2, Day 2 Activity 3). They identify unit rates as the slope (k in y = kx), check whether a graph is a straight line through the origin, and compare steepness of lines to decide which rate is larger (Activities 4 and 5). Several tasks ask students to determine whether plotted data form a straight line and to label independent and dependent variables when graphing real-world quantities (Activities 6 and 7).

Students write and interpret equations of the form y = kx and t = p × n and are explicitly told that a proportional relationship graphs as a straight line through the origin. Activities and quiz items require students to read graphs, identify unit rates from lines (for example the Tank A vs Tank B comparison), and decide whether tables or plotted lines represent proportional relationships. Several tasks ask students to create graphs, find unit rates from plotted lines, and compare steepness, which models quantitative relationships with straight lines.

Students are asked to examine graphs (for example, multiple "Hours Worked vs. Money Earned" graphs with plotted points such as (0,0),(8,36),(15,60) and (0,0),(1,6.80),(2,13.60),...) and to determine or circle whether the graph represents a proportional relationship. Several problems require students to decide from tables or plotted points whether a relationship is proportional (e.g., tables with one value off the line and problems that ask "Yes, it's proportional" or "No, it is not proportional"). Students are asked to graph equations like y = 4x or y = 5x and describe the relationship, reinforcing that straight lines represent these quantitative relationships.

Students are instructed to graph number of lemons (x) versus total cost (y) and to "plot a line for each grocery store, showing how the price increases as you buy more lemons." Students answer graph-interpretation questions asking which line is steepest, which is least steep, what steepness tells about price per lemon, and how to tell which store offers better value by looking at the graph. In Part 2 students create tables, plot data points for proportional relationships, produce graphs that show straight lines through the origin, and write equations in the form y = kx to model the relationships.

Students write and use linear equations relating two quantities, for example Total Cost = Fixed Cost + (Variable Cost × # of Items) and Selling Price = Wholesale Price × (1 + Markup Rate). Students set up and solve equations for unknowns (e.g., solve 25 + 3r = 58 to find r = 11) and use one-step formulas to compute outputs from inputs in multiple practice problems. Activities have students translate real-world situations (rides, prices, markups) into expressions and compute corresponding numeric pairs.

Students model quantitative relationships with straight lines in multiple real-world examples (earnings $10/hour, distance vs. time, price per pound) and plot points from tables and equations (y = kx). Students create tables of values, plot points, connect them with a ruler, and compute the constant of proportionality by dividing y by x to write equations from graphs. Activities ask students to decide whether given graphs are proportional (straight line through the origin) and to identify the unit rate. Students also translate between equations and graphs and practice graphing lines from equations such as y = 3x and y = 1/2 x.

Students create tables of paired quantitative values (time vs. distance, weeks vs. dollars saved, cups of milk vs. cups of flour) and plot those points on coordinate grids. They write and use equations in the form y = mx to represent relationships and identify m as the slope/unit rate. Students use the Two-Point Formula and pick two plotted points to calculate slope and are instructed to use a ruler to draw straight lines through plotted points (e.g., graphing savings plans, jar-marble rates, and book stacks). Several activities ask students to graph two relationships on the same axes and compare which line is steeper.

Students are asked to examine a graph showing several plotted points that "lie close to or on what might be a straight line," pick pairs of points, draw right triangles, and compute rise and run (Activity 2, Step 1). They draw and compare right triangles (Activity 2, Step 2) and set up proportions to decide whether triangles are similar, using that result to conclude whether points lie on the same straight line. The lesson includes an image with points that lie on a line and one point off the line (an outlier), which students use to judge whether the points form a straight line.

Students practice representing quantitative relationships with straight lines by writing and graphing equations in slope-intercept form (y = mx + b) and by converting standard-form equations into y = mx + b. Students find slope from two points (m = change in y / change in x), use tables of values to determine m and b, and graph real-world scenarios (e.g., earnings, costs) as linear functions. Students plot given points and extend lines through those points (Extend the Line, Solving for b) to produce and compare straight-line models.

Students are given multiple table-to-graph tasks (e.g., babysitting earnings, car rental, dog walker, lawn care) where they determine if a relationship is proportional, find slope and y-intercept, write the equation, and graph the data. Several problems require students to identify slope from plotted points, extend a given line to find the y-intercept, and write the equation of that line. Other tasks ask students to graph two lines from coordinates and compare rates of change, and to decide which graphs represent proportional (origin-passing) linear relationships.

Students plot distance vs. time and cost vs. distance on coordinate graphs (Step 4: Graph It! and the Cost graph) and write linear equations for each mode of travel (y = mx for speed; y = mx + b for cost). Students compare slopes, identify which line is steepest, determine proportionality, and answer questions such as "Do all lines represent a linear relationship?" and "Which method has the steepest slope?". The answer keys and activities require students to graph multiple quantitative variables on the same axes and to use the straight-line equations to model those relationships.

The lesson has students plot (x,y) pairs from tables and equations and observe when those points form a straight line (e.g., Activity 3 and Graph Example 1 with y = 2x + 1). Students learn that a linear function creates a straight line and that linear functions change at a constant rate, and they practice graphing linear rules and connecting points to produce lines. Several activities require students to complete tables, plot points on coordinate grids, and match tables to linear graphs, reinforcing that straight lines represent relationships between two quantitative variables.

Students examine tables of (x,y) values and compute successive differences to identify constant rate of change, indicating linear vs nonlinear. Students fill tables by evaluating equations (e.g., y = 2x + 4, y = x^2), plot points from those tables, and label graphs as straight lines or curves. Several activity pages ask students to decide "Linear or Nonlinear?" for graphs and tables and include examples of straight-line graphs (e.g., y = 2x, y = −x + 1) and nonlinear graphs (e.g., y = x^2).

Students repeatedly identify whether a graph is straight or curved and whether it is increasing, decreasing, or constant (Graph Matching, Part 3, and Describing Graphs). Students plot points from real-world descriptions (Sylvia the Sloth, Timmy the Turtle, Bella's Balloon) and connect those points to produce straight-line segments that represent constant rates. Students match straight-line graphs to scenarios (e.g., money earned per hour, constant increase/decrease), showing that straight lines are used to model constant-rate relationships between two quantitative variables.

Students convert between tables, graphs, and equations representing two quantities (for example, tables of minutes and miles) and write equations in y = mx + b. Multiple activities ask students to find slope from two points or from a table, identify the y-intercept, and graph the corresponding straight line (e.g., Ellie's subway trips modeled as y = 2x + 2). Students also practice rewriting standard-form equations into slope-intercept form and then graphing those lines.

Students identify and model relationships between two quantitative variables by naming inputs and outputs and writing linear functions in the form output = slope × input + starting value from stories, tables, and line graphs. Students calculate slope using the slope formula by selecting two clear points on a line and determine the y-intercept from table or graph values. Students convert tables of values and plotted lines into function rules (e.g., P = 15h, C = 3h + 5) and practice interpreting slope and starting value in context.

Students repeatedly work with straight-line relationships presented as graphs, tables, equations, and verbal descriptions (e.g., distance vs. time, money over weeks). Students calculate slopes from two points, identify y-intercepts as starting values, and compare which linear situation changes faster. Students also read multi-line graphs to compare starting points and rates of change without computing equations.

Students calculate slopes and intercepts from equations, tables, and graphs (e.g., find slope from a plotted line, determine rate of change from a time-distance table, and write equations like E=12h or y=4x-3). Students match piecewise linear graphs to real-world stories (car and hiker distance-time scenarios) and analyze multi-line graphs (streaming subscription costs) to identify starting values and which line increases fastest. Several activity images show plotted points on or along straight lines and ask students to identify the slope or y-intercept from those graphs.

Students design and solve graph-based problems (red cards) that ask whether a graph is linear or nonlinear, identify slope, and match graphs to situations. The project asks students to construct functions to model linear relationships, determine rate of change and initial value from graphs or tables, and write equations from real-world descriptions (blue and yellow cards). Students create tables (green cards) and write equations from those tables, reinforcing forming linear models from paired x,y values.

Students are asked to graph two linear equations on coordinate grids to visually estimate their intersection (for example, graphing 3x - 2y = 7 and x + y = 4 and comparing the graph estimate to a substitution solution). The lesson repeatedly has students rewrite equations in slope-intercept form, plot lines, and identify the point where the lines intersect as the solution. The Desmos section instructs students to enter equations and observe where two lines cross, reinforcing that straight lines represent relationships between two quantitative variables.

Students write linear equations in slope-intercept form (y = mx + b) to model relationships such as cost vs. quantity and rate × time problems. Students set up and solve systems of linear equations to find break-even points and intersections (e.g., y = 20x + 50 and y = 30x leading to (5,150)). Students graph linear equations to visualize solutions and compare options, with prompts to create graphs of both lines to see the picture of the solution.

Students graph linear equations (e.g., "Graph y = 2x - 1", multiple graphing exercises) and compute slope from two points (several problems ask for slope through given points). Students write equations of lines from two points and solve real-world problems that set up linear relationships (hourly pay + bonus, ticket costs) using linear equations. Several items ask students to interpret intersections or classify systems as one/none/infinite solutions by inspecting graphs.

Students write linear cost equations (e.g., C = 1200m, C = 1500 + 1050m; C = 225 + 0.60x; C = 5 + 1.5h) and use tables of values to compute points. Students graph those equations on coordinate grids, label axes, plot lines, and identify intersections/break-even points. In the Meal Plans activity students analyze a provided graph to find y-intercepts and slopes (fixed costs and cost per week) and then write equations from those line features.

Students are explicitly instructed about best fit lines in Day 2 Activity 3, including a definition that a best fit line is a straight line that runs through the middle of the data and guidelines such as having about half the points above and half below. Multiple student activities ask learners to choose the best-fit line from options, draw their own best-fit line (Part 3), and extend the line to make predictions (Activity 6). The lesson also has a detailed section on variability that asks students to judge how closely points cluster around the line and to compare graphs for higher or lower variability.

Students plot pairs of quantitative data (hours vs. grades, height vs. arm span, temperature vs. ice cream sales, etc.) and are repeatedly asked to determine whether there is a linear relationship and to make predictions from that pattern. Students are instructed to "Draw a best fit line (if needed)" and to answer prompts such as "Is there a linear relationship? How do you know?" and "Are there any outliers?", which require judging how closely points lie to a straight line. Answer keys describe points "cluster[ing] around a straight line" and identify when points do or do not fit the line, showing students practice informal assessment of model fit.

Students practice fitting straight lines to scatterplots by choosing the equation that matches a plotted best‑fit line (Activity 1) and by writing equations from lines shown on graphs (Activity 1 Part 2 and multiple student pages). Students draw a best‑fit line, select two points on that line to compute slope, form y = mx + b, and interpret slope and intercept in context (Activity 2 examples, Bird Migration activity). Students use those linear models to make predictions and solve real‑world problems (ice cream example, plant growth, tickets sold, etc.).

Students are asked to decide whether relationships are linear and to identify positive or negative association on multiple scatterplots (e.g., Study Time vs Test Scores, Hours Practiced vs Performance, Hours of Video Games vs Homework). Several items require students to choose which of three drawn lines best represents a relationship (e.g., Temperature vs Ice Cream Sales; Hours of Sunshine vs Sunglasses Sold) and to explain why one line is better. Other tasks ask students to write or choose a linear equation that fits a scatterplot (Question 13: choose between y=2x+4 or y=4x+0; Question 14: write an equation) and to make predictions from trends on scatterplots.

Students are instructed to label axes, set up a graph, plot each data pair, and answer analysis questions about patterns and trends (Part 4: Make Your Scatterplot, Steps 1–4). The materials show a sample scatterplot with a drawn line of best fit and explicitly tell students to "draw a line that best fits the overall shape of the data if a pattern is clear." The Parent Plan Skills list explicitly names the practice of using straight lines to model relationships and informally fitting a straight line to scatterplots that suggest linear association.

Students are asked to graph equations such as y = 6x, label at least three points, and circle the point where the line crosses the origin (Activity 3). Students determine which of several given graphs are proportional, identify constants of proportionality, and create their own equation, table, and graph to represent a proportional relationship. Activity 2 and the parent plan prompt students to interpret graphs and match tables with linear equations (e.g., distinguishing y = mx from y = x + b), and an included image shows a diagonal line on a coordinate grid.

Students plot and interpret linear relationships from tables and graphs (for example, the babysitting pay and car rental tables with points at (0,0),(1,14),(2,28) and (0,0),(1,75),(2,150)). Students write equations in the form y = mx + b and identify slope and y-intercept from points, tables, and graphs (Activities 2 and 3 ask for equations, slope, and intercept identification). Students compare lines and use steepness to determine which relationship has a greater rate of change (Activity 4 asks students to graph and compare rates of change between lines and plans).

Students are asked to graph and interpret straight-line equations (e.g., "Graph the equation y = 4x and describe the relationship," and graph lines passing through given points such as (0,0) and (4,-8)). Students calculate and interpret unit rate/slope from lines (e.g., find unit rate for a line through (0,0) and (2,10); several problems ask for slope, intercept, and which line has greater rate of change). The materials include an image of a coordinate grid with plotted points and a straight line drawn through them, showing a visual of points with a line.

Students practice recognizing and creating linear functions from situations (Activity 4: write y = 18h; Activity 2: taxi fee modeled by y = 12x + 10). Students compute and interpret slope and intercept and graph straight lines (Activity 3: find slope from two points, graph y = 3x - 2, and an image showing points on a line). Students distinguish linear vs. nonlinear equations and interpret what a line's slope and intercept represent in context.

Students analyze scatterplots in Activity 3 by identifying types of correlation (positive, negative, none) and interpreting what the relationships suggest. The activity asks students to think about and interpret lines of best fit (e.g., "What does it mean if most data points are close to the line of best fit?"). The Parent Plan and skills list explicitly state that students will interpret lines of best fit and investigate patterns of association in bivariate data.

Students analyze a scatter plot of hours studied versus test score (Question 46) and are asked to name the type of correlation and interpret what it suggests. Question 47 directly asks what it means if most data points are close to the line of best fit. The answer key states that the data closely follows the model and that the line of best fit represents the relationship well, tying the scatter-plot interpretation to a linear model.