Free Printable Matching Equations and Graphs Worksheets for Year 7

In 7th grade, the focus is on proportional relationships. Students learn to recognize that the graph of a proportional relationship is a straight line that passes through the origin (0,0). They match equations in the form y = kx to their corresponding graphs by identifying the constant of proportionality, or unit rate (k), from the graph.

Show students a line representing a proportional relationship, like the cost of multiple items. Ask them to find the point (1, r), where 'r' is the unit rate (the cost of one item). Explain that this point reveals the constant of proportionality, k, in the equation y = kx. Practice with several examples, having them articulate what the point (1, k) means in the context of the problem.

Good practice problems ask students to do more than just match. Provide a graph of a proportional relationship and ask them to write the corresponding equation. Conversely, give them an equation like y = 3.5x and have them identify which of several graphs represents it. Word problems that require students to graph a relationship and then write its equation are also highly effective.

A common mistake is confusing the x and y axes when calculating the unit rate, leading to the reciprocal of the correct value (e.g., calculating x/y instead of y/x). Students may also incorrectly identify a relationship as proportional if the line does not pass through the origin, or they might struggle to find the unit rate when the point (1, k) is not explicitly labeled.

Wayground offers multiple formats to suit your needs. You can host the worksheet as an interactive quiz on the platform for immediate feedback, or download the printable PDF for students to complete on paper. An answer key is included with every worksheet. If you use the printable version, the Wayground for Teachers app allows you to quickly scan and grade the completed worksheets.

This topic is central to the Ratios and Proportional Relationships (RP) domain in the 7th-grade Common Core standards. Specifically, students learn to recognize and represent proportional relationships between quantities (7.RP.A.2). These worksheets provide practice in deciding whether two quantities are in a proportional relationship by graphing them and observing if the graph is a straight line through the origin, and identifying the constant of proportionality (unit rate) from graphs.