# Linear Equations

linear equations
Building px + q = r equations from situations.
7-EE.B.4a, G.B.4

Click on the image at right to get the lesson app with instructor notes. Or you can install right from here by clicking the logo below:

In this lesson app, students will learn a process they can use to create an equation to represent a linear relationship. Students will identify the proportion that represents the rate of change, then they cross multiply and isolate to write the equation in the form px + q = r, and finally, they add (a positive or negative) to adjust for the initial, or starting, value in the problem situation.

In Module 2, students operate with negative integers. However, no operations are necessary. Students write absolute value expressions to indicate coordinate plane distances. The main ideas are that polygons can be drawn on the coordinate plane and distances between horizontal and vertical points can be determined by subtracting coordinates.

Finally, in Module 3, students learn the formulas for the circumference of a circle and the area of a circle. Students then apply these formulas in solving different problems. Students are also asked to generalize about how doubling the radius affects both the circumference and the area of a circle.

Module 1 Video

The video for this lesson shows how degrees Celsius (x) is related to degrees Fahrenheit (y) by the equation $$\mathtt{y = \frac{9}{5}x + 32}$$. The video demonstrates how to build this equation by considering the rate of change (for every 5°C increase there is a 9°F increase) and the intercept (y = 32 when x = 0). The language of intercept and rate of change is not used in the video.