Students examine graphs in Activity 3 to decide whether a graph represents a proportional relationship by checking whether a line is straight and passes through the origin. Students pick points on plotted lines and compute k = y/x to identify the constant of proportionality from graphs (e.g., find k = 2/5 or k = 6/1). Students also compare multiple lines (e.g., lines A and B) to identify which line is proportional and write the corresponding k value.

Students are asked to decide whether graphs are straight and pass through (0,0) and to test constant rates from tables (Activities: Analyzing Graphs; Is it a Proportional Relationship; Graphing to Test Proportionality). Students plot points from tables and equations and draw lines (Activities: Graphing Equations; Graphing Proportional Relationships from Tables), and they sketch graphs from verbal descriptions such as a train at 80 mph, a car at 65 mph, or saving $5 per week (Graphing Scenarios; Challenge problems). Students compare lines by steepness and determine which is fastest or which has the higher unit rate using graphs (Comparing Proportional Relationships).

Students are asked to interpret graphs and use graph features to find unit rates (e.g., Quiz items that ask students to determine unit rate from a graphed proportional relationship and the Water Tanks Filling Over Time question asking which tank fills faster). Students are explicitly taught that a proportional relationship graphs as a straight line through the origin and asked to identify whether graphs represent proportional relationships (multiple quiz and activity items). Students are prompted to model situations and create graphs, for example the Theme Park Tickets challenge asks students to model cost, create a graph, and describe proportionality.

Students graph linear equations (e.g., "Graph the equation y = 4x" and "Graph the equation y = 5x") and are asked to describe the relationship shown. Students analyze plotted graphs such as "Hours Worked vs. Money Earned" and decide whether the graph represents a proportional relationship (circle proportional / not proportional). Students interpret and explain special points on proportional graphs (for example, what (0,0) and (1,r) represent) and find constants of proportionality from tables and graphs.

Students create graphs of number of lemons (x) vs total cost (y), label axes, and plot lines for each store and pricing option (individual and bulk). They answer guided questions about which plotted line is steepest or least steep and explain that steepness relates to price per lemon. In the recipe/proportions section, students translate the verbal rule (e.g., 2 tablespoons per cup) into a table, graph the resulting points, and write the equation in the form y = kx, producing straight-line graphs through the origin.

Students analyze multiple graphs to decide whether relationships are proportional, explaining reasoning and identifying unit rates (Activity 1 graphs A–D and accompanying student pages). Students turn equations into graphs by making tables, plotting points, and deciding proportionality (Day 2 Activity 3), and they convert graphs into equations by picking non-origin points and computing k = y/x (Activity 4). Students also work with negative-slope equations and a hands-on "Walk the Graph" activity that has them move down for negative k, which exposes them to linear increasing and decreasing behavior in specific proportional cases.

Students repeatedly create graphs from verbal descriptions and equations (e.g., graphing y = 3x and y = 5x for book stacks, y = 50x and y = 60x for cars, and y = 0.6x and y = x for faucets). Students calculate and interpret slope from tables, graphs, and equations (Activity 3 uses the two-point formula and examples showing rise/run and slope = m). Students compare increasing versus decreasing relationships and signs of slope (Part 3 includes y = -3x and asks what a negative unit rate indicates about direction).

Students identify x- and y-intercepts from given graphs and write them as ordered pairs in multiple activities and answer keys. Students plot given intercepts on empty coordinate planes and connect the points with a straight line to sketch the graph (lines E–H and several graphing problems). Students work with linear equations (y = mx + b and examples like 2x + 4y = 8) and note that these equations produce straight-line graphs.

Students pick two lattice points on given graphs, draw right triangles between them, and count rise and run to compute slope (m = rise/run). The materials include upward- and downward-sloping lines and explicit direction rules (up/right positive, down/left negative), so students determine sign of slope and whether a line is increasing or decreasing. In Activity 2 students set up proportions comparing rise/run for different triangles to decide whether points lie on the same straight line, practicing identification of linear vs. non-linear (not-all-points-collinear) situations.

Students graph many lines in slope-intercept form and compare their steepness and direction (Activity 1, Activity 3, Activity 4). They analyze graphs to determine whether a line increases, decreases, or is flat (positive, negative, zero slope) and answer questions like which line is steepest or which goes down the fastest. Students convert tables and real-world verbal descriptions into linear equations and then sketch those equations on coordinate grids (Activities 7 and 8). Several tasks ask students to identify which real-world scenario a given graph represents, requiring interpretation of a graph's qualitative features.

Students are asked to graph data from tables and equations (e.g., babysitting/car rental, dog walker/lawn care, and lines given by coordinates) and to find slope and y-intercept from graphs and equations. Several problems require students to determine whether a relationship is proportional (passes through the origin) and to compare rates of change between two lines. Tasks also ask students to identify positive vs. negative slope (interpreting upward/downward lines) and to extend a plotted line to find the y-intercept.

Students plot distance vs. time for car, train, and plane using given speeds (y = mx) and fill tables of time and distance, then graph all three lines on the same axes. Students answer questions that require analyzing their graphs qualitatively (e.g., which is slowest/fastest, identifying rise/run for the train, and explaining that steeper slope means higher speed). In the cost unit, students write linear cost equations (y = mx + b), graph them, and interpret features such as which line has the steepest slope and which has the larger fixed cost (y-intercept).

Students practice identifying functions from graphs using the Vertical Line Test and are asked to distinguish linear versus non-linear graphs (several examples describe lines rising or with negative slope and parabolic curves). Students create tables from rules (including rules written in words), plot input/output pairs, and connect points to observe whether the result is a straight line or a curve (Activities 3 and 4). The materials explicitly state and have students observe that linear functions change at a constant rate and that positive/negative slope makes the graph rise or fall, and students match tables to given graphs to reinforce graph-shape recognition.

Students examine multiple graphs and tables and are asked to decide whether each relationship is linear or nonlinear by checking the rate of change in tables and the shape (straight line vs curve) in graphs. Students complete tables by plugging x-values into given equations (e.g., y = 2x + 4, y = x^2) and calculate y2−y1/x2−x1 to determine constant or changing rates. The materials include pictured examples with descriptive language (a line with positive slope, a parabola getting steeper) and activity pages where students plot points from equations and label graphs as linear or nonlinear.

Students repeatedly analyze graphs to decide whether the line is straight or curved and whether it is increasing, decreasing, or constant (Graph Matching, Part 2 and Part 3 activities). In Activity 3 students write sentence descriptions of given graphs, identifying rising, flat, and falling intervals and interpreting real-world meaning (fountain, park visitors, skateboarder, sunflower growth). In Activity 2 students are given verbal, real-world scenarios (Sylvia the Sloth, Timmy the Turtle, Bella's Balloon Ride) and are instructed to plot points, connect them, and produce graphs that match the verbal descriptions.

Students plot points and connect them to form straight lines in multiple activities (e.g., Activity 1 "What Is Slope?" and the graph exercises), and they calculate slope from two points using m = (y2 - y1)/(x2 - x1) (Activity 4). Students examine graphs to decide whether a line goes up or down and label slopes as positive, negative, zero, or undefined (Activity 2 and Activity 3). Students also find slope from tables and equations, using those representations to determine whether y increases or decreases as x increases (Activity 5 and Activity 6).

Students repeatedly identify the y-intercept and compute the slope from graphs, tables, and pairs of points (e.g., Activity 1 finds b = 2 and m = 2 from points A(0,2) and B(3,8)). Multiple activities require students to read an equation y = mx + b, plot the y-intercept, use rise/run to place another point, and draw the line (Activity 2 and Equation to Graph pages). Answer keys and examples call out positive and negative slopes and instruct students to interpret rise/run (e.g., slope = 3 means rise 3, run 1; life-application notes say positive slope = uphill, negative = downhill).

Students analyze tables and line graphs to find rate of change and starting value (for example, Table Example 1 has hours vs. pages read where students identify a slope of 15 and a y-intercept of 0). In Case File 003 students use two points from a plotted straight line (e.g., (0,5) and (1,8)) to compute slope with the slope formula and interpret the y-intercept as a starting cost, then write a linear function C = 3h + 5. Multiple scenarios (stickers, bus passengers, phone battery) include negative slopes and prompt students to describe quantities as increasing or decreasing and to write matching linear equations.

Students explicitly compare rates of change and starting values across representations (graphs, tables, equations, verbal descriptions) in multiple examples (e.g., walking pace example comparing a verbal description to Bella's graph; sneaker sales and bank account examples where slopes and y-intercepts are identified). Students interpret multi-line graphs and answer qualitative questions such as who traveled faster, when lines intersect, which group changed faster, and which had the most steady pace (Interpreting Graphs activities). Students also reason about increasing versus decreasing situations (e.g., plant growth and accounts losing money) by using slope signs and visual slopes on graphs.

The Skills list explicitly names "Describe qualitatively the functional relationship between two quantities by analyzing a graph" and includes the instruction to "Sketch a graph that exhibits the qualitative features of a function that has been described verbally." Several student tasks ask learners to analyze graphs: Q18 asks students to match a verbal car-distance story to one of three graphs and explain their reasoning; Q23 (streaming costs) and the water temperature problems require students to identify starting fees, fastest increases, and compare rates from graphs. Other problems ask students to use the vertical line test, decide whether a graph is linear or nonlinear, interpret slope (including slope = 0), and compare rates of change from tables and graphs.

Students create 12 red "Graph Cards" that require them to draw or glue small graphs and answer questions such as "Is this a function?", "Is the graph linear or nonlinear?", and "What is the slope of this line?". Yellow description cards ask students to match verbal scenarios to graphs or tables and to identify the rate of change from a story. Green and blue card tasks also require matching between representations (tables, equations, graphs), reinforcing analysis of graphs against other formats.

Students plot and graph equations in slope-intercept form (y = mx + b) and use rise/run to place points (for example y = 2x + 3 and y = -x + 3). They convert equations into slope-intercept form and compare slopes to determine whether lines will intersect, be parallel, or coincide (e.g., converting 4x−2y=8 and 2x−y=4 to y=2x−4). Students draw lines on blank coordinate grids to produce one solution, no solution, or infinite solutions and substitute intersection coordinates into both equations to verify solutions.

Students plot lines from two given points, write equations in slope-intercept form, and use graphs to estimate intersection points. Students describe slopes as rising or falling (positive or negative) when they draw lines and note whether lines are parallel, intersecting, or overlapping. Students analyze graphs to determine the number of solutions (one, none, infinite) and connect graph points to solutions of the equations.

Students are asked to use and graph linear equations in break-even contexts (e.g., the apple price graph and the cleaning/streaming examples) and are shown how to write functions in slope-intercept form (y = mx + b). The lesson tells students they can "create a graph of both lines to see a picture of the solution" and uses the graph to interpret which option is cheaper before and after the intersection. Activity pages guide students to write systems for cost vs. quantity and to find the intersection (break-even) both algebraically and with reference to a graph.

Students plot points, graph linear equations (e.g., y = 2x − 1, y = −3x + 2), and compute slopes from two given points (several problems ask for slope through two points). Students graph pairs of linear equations and determine intersections or conclude systems have no solution or infinitely many solutions. Images and problems label slopes and y-intercepts and show intersecting and parallel lines, and students write the solution point when lines meet.

Students write cost equations from verbal descriptions (housing, transportation, streaming, meal plans, phone plans) and then graph those equations, label axes, and plot both lines to compare costs. Students set linear equations equal and solve for break-even points and mark intersections on graphs (housing, transportation, streaming). Students analyze graphs to identify y-intercepts and slopes (Meal Plans activity asks for initial cost and cost per week) and note when two equations represent the same line (Phone Plans activity).

Students repeatedly identify independent and dependent variables and classify relationships as positive, negative, or no relationship and as linear or non‑linear (e.g., Scatterplot Notes, matching scatterplots to scenarios). Students locate clusters and outliers and describe variability around a trend. Students draw, choose, and evaluate best‑fit lines, compare variability between graphs, and extend lines to make predictions (Best Fit Line, Draw Your Own Best Fit Line, Making Predictions).

Students plot real bivariate data (hours studied vs. grade; height vs. arm span; temperature vs. ice creams sold; minutes of exercise vs. resting heart rate, etc.) and answer questions about whether the scatterplot shows a linear relationship, whether it is increasing or decreasing, and whether there are clusters or outliers. Multiple activities ask students to choose axes, scales, labels, plot points, draw a best‑fit line, and verbally describe trends (e.g., "As hours studied increase, test grades increase" or "negative linear relationship"). Other tasks require students to match written scenarios to given scatterplots and to invent or select real‑world stories that fit unlabeled scatterplots, reinforcing identification of positive/negative, linear/nonlinear, and random patterns.

Students repeatedly read scatterplots and match or write the equation of the best-fit line, identifying slope and y-intercept (multiple-choice graphs, Part 2 write-the-equation tasks, and the answer key). Students interpret those equations in words and state independent and dependent variables (ice cream example: "For each 1°F increase, 2 additional cones are sold; when x=0, 50 cones are sold"). Students plot collected data and draw a best-fit line (Bird Migration activity) and compute the rate of change from two points to form a linear model and make predictions.

Students repeatedly analyze graphs and scatterplots to describe relationships: several items ask whether a relationship is linear or nonlinear and whether it is positive, negative, or none (e.g., Exercise 5: Hours Practiced vs. Piano Performance Score; multiple scatterplot questions asking linear/nonlinear and positive/negative). Students identify increasing/decreasing trends and variability, locate clusters and outliers (Exercises 6, caffeine vs. sleep; social media vs. texts; missing assignments vs. test score), and choose or judge which line best fits a displayed relationship (Hours of Sunshine vs. Sunglasses Sold; temperature vs. ice cream sales). Students also draw scatterplots from given data, label axes, and predict values from plotted trends using blank grids provided on multiple pages.

Students are instructed to create scatterplots: they label axes, choose scales, plot paired numerical data, and are prompted to analyze what they notice (e.g., "Do the dots form a pattern?" and "Is there a trend?"). The materials ask students to identify positive/negative/no correlation, note clustering and outliers, and optionally draw a line that best fits the data. The parent/planning notes explicitly tell students to informally fit a straight line for scatter plots that suggest a linear association and to judge closeness of data points to that line.

Students graph linear equations such as y = 6x, label at least three points, and circle the origin. Students identify which graphs are proportional (selecting graphs A, B, or C) and determine the constant of proportionality. Students interpret specific points on graphs (for example, explaining what (0,0) and (1,6) represent) and read values from graphs (e.g., total cost for 0, 2, 4, 6, 8 pieces). Students create a proportional relationship by writing an equation, making a table, graphing the relationship, and explaining what the graph represents.

Students analyze graphs to find slopes and interpret whether a relationship is increasing or decreasing (e.g., problems asking for slope, identification of y-intercept, and interpretation such as the delivery service and the line passing through (0,0)). Students determine proportionality and whether a graph passes through the origin (Activity 2 asks "Is this relationship proportional?" and asks what (0,0) represents). Students translate verbal descriptions into equations and then sketch or graph them (e.g., babysitting pay, car rental costs, job offers with hourly rates and bonuses where students write equations and graph both lines).

Students are asked to graph linear equations and describe relationships (Problem 20: "Graph the equation y = 4x and describe the relationship"). Students identify positive versus negative slopes from a plotted graph (Problem 31 asks which line has positive slope and which has negative). Students plot lines from given points and compare rates of change (Problem 35 gives point sets for Line A and Line B and asks which has a greater rate of change), and students plot a line through given points and find its slope and equation (Problem 37 asks to plot the line through (0,0) and (4,-8) and find slope and equation). The answer key and image also describe the proportional linear relationship and interpret slope as rise/run for y = 4x.

Students analyze graphs to decide whether relations are functions using the vertical line test (Activity 1) and explain reasoning. Students are asked to tell from a graph whether a function is nonlinear and to explain how they know (Activity 2, "Graph Clues"). Students determine whether relationships are increasing or decreasing from slopes and equations and graph linear equations (Activity 3 asks for the slope, whether the relationship is increasing or decreasing, and to graph y = 3x − 2).

Students graph linear equations such as y = x - 3 and y = -2x + 1 and work with coordinate grids to produce those lines. Students compute slope from two given points (e.g., (3,2) and (7,10)) and use slope-intercept form to graph lines. Students also interpret graphs of pairs of lines to find intersection points when solving systems.

Students analyze scatterplots in Activity 3, answering questions that ask them to identify positive, negative, or no correlation and to explain what the relationship suggests. The Parent Plan and Activity 3 explicitly have students interpret lines of best fit and recognize linear versus nonlinear association, including judging how close points are to a line to assess linear trends. Students also practice distinguishing correlation from causation and interpreting what trends imply about the relationship between two quantities.

Students are asked explicitly to distinguish linear vs. nonlinear from a graph (Question 2) and to identify a nonlinear equation from a list (Question 1). They compute slope (Question 5), find intercepts from equations and tables (Questions 3–4, 9a), and graph a linear equation y = 2x − 4 (Question 6). Students apply the vertical line test to decide if a graph is a function (Question 7) and interpret a scatter plot by naming the type of correlation and what it suggests (Question 46).