Graph Proportional Relationships From Equations

Begin with the two reading sheets so students connect slope and unit rate. Then move to graphing and finish with the comparison sheet.

Complete tables for equations like y = 3x and y = 2/3x, graph each line and label the point (1, k). In a proportional relationship y = kx, the graph is a line through the origin, and k is the unit rate and the slope of the line. The directions on the page read: Complete the table for each equation. Plot the points, draw the line through the origin and the points, then plot and label the unit rate point (1, k). An answer key is included.

Yes, both. We made it for 8th grade linear equations, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

The line passes through (0, 0) and (1, k), so it rises k units for each 1 unit it runs. That rise over run is the slope, and it is also the amount for one unit. On the apples graph, it is the cost of one pound.

It means zero of one quantity matches zero of the other, such as 0 hours worked and 0 dollars earned. What Points Mean on a Proportional Graph asks students to explain this point for each graph.

Find the unit rate of each one, whether it comes from a graph, a table, an equation or a sentence. Compare the two numbers with units. Compare Two Proportional Relationships also asks by how much one is greater.