Section	Teacher-facing learning goals
Proportional relationships	Lesson 1 Comprehend that for the equation of a proportional relationship given by \(y=kx\), \(k\) represents the constant of proportionality. Create graphs and equations of proportional relationships in context, including an appropriate scale. Interpret diagrams or graphs of proportional relationships in context. Lesson 2 Compare graphs that represent the same proportional relationship using differently scaled axes. Create graphs representing the same proportional relationship using differently scaled axes, and identify which graph to use to answer specific questions. Lesson 3 Create an equation and a graph to represent proportional relationships, including an appropriate scale and axes. Determine what information is needed to create graphs that represent proportional relationships. Ask questions to elicit that information. Lesson 4 Compare the rates of change for two proportional relationships, given multiple representations. Interpret multiple representations of a proportional relationship in order to answer questions (in writing), and explain the solution method. Present a comparison of two proportional relationships (using words and multiple other representations).
Representing Linear Relationships	Lesson 5 Compare and contrast (orally and in writing) proportional and non-proportional linear relationships. Interpret (orally and in writing) features of the graph (i.e., slope and \(y\)-intercept) of a non-proportional linear relationship. Lesson 6 Describe (orally and in writing) how the slope and vertical intercept influence the graph of a line. Identify and interpret the positive vertical intercept of the graph of a linear relationship. Lesson 7 Create an equation that represents a linear relationship. Generalize (orally and in writing) a method for calculating slope based on coordinates of two points. Interpret the slope and \(y\)-intercept of the graph of a line in context. Lesson 8 Coordinate (orally) features of the equation \(y=b+mx\) to the graph, including lines with a negative \(y\)-intercept. Create and compare (orally and in writing) graphs that represent linear relationships with the same rate of change but different initial values.
Finding Slopes	Lesson 9 Create a graph of a line representing a linear relationship with a non-positive rate of change. Interpret the slope of a non-increasing line in context. Lesson 10 Create a graph of a line using a verbal description of its features. Describe (orally) the graph of a line using formal or informal language precisely enough to identify a unique line. Generate a method to find slope values given two points on the line. Lesson 11 Comprehend that for the graph of a vertical or horizontal line, one variable does not vary, while the other can take any value. Create multiple representations of linear relationship, including a graph, equation, and table. Generalize (in writing) that a set of points of the form \((x,b)\) satisfy the equation \(y=b\) and that a set of points of the form \((a,y)\) satisfy the equation \(x=a\).
Linear Equations	Lesson 12 Comprehend that the points that lie on the graph of an equation represent exactly the solution set of the equation of the line (i.e., that every point on the line is a solution, and any point not on the line is not a solution). Create a graph and an equation in the form \(Ax+By=C\) that represent a linear relationship. Determine pairs of values that satisfy or do not satisfy a linear relationship using an equation or graph. Lesson 13 Calculate the solution to a linear equation given one variable, and explain (orally) the solution method. Determine whether a point is a solution to an equation of a line using a graph of the line.
Let's Put It To Work	Lesson 14 Describe (orally) limitations of a graphical representation of a situation based on real-world constraints on the quantities. Interpret the graph of a linear equation in context, including slope, intercept, and solution, in contexts using multiple representations of non-proportional linear relationships.

8.3 Linear Relationships