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Chapter 3: Q. 4 (page 176)

Find the equation of the line containing the points (-1, 4) and (2, -2). Express your answer in slope–intercept form and graph the line.

Short Answer

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Step by step solution

01

Step 1. Given information.

Find the equation of the line containing the points (-1, 4) and (2, -2). Express your answer in slope–intercept form and graph the line.

02

Step 2. Definition.

The equation of line ( in slope - intercept form) is given by:

y=mx+b;m≠0

The slope of the graph is mand y- intercept is b . The average rate of change is equal to slope:

m=y2-y1x2-x1

03

Step 3. Equation of line.

Slope:

A=x1,y1=-1,4B=x2,y2=2,-2

m=y2-y1x2-x1=-2-42-(-1)=-63=-2

So, the slope is m=-2.

Y - intercept:

The point (2,-2) is on the, because we want to find b, put the coordinates of the points inside the equation:

y=mx+b-2=-2·2+b-2=-4+bb=-2+4b=2

So the equation of line is:

y=-2x+2

04

Step 4. Graph the equation of line. 

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Most popular questions from this chapter

List the intercepts of the equation y=x2-9.

In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

In Problems 7–22, solve each inequality.

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