Chapter 4, Problem 1CR

To determine

Write an equation of the line in slope-intercept form.

Answer to Problem 1CR

The equation of the line is $y=-x/2+1.$

Explanation of Solution

Given information: The graph is given below.

  

From the graph the line is passes through the points (0,1) , (2,0), (4,-1).

Calculation:

Formula :

In general slope intercept equation of a line is,

  $y=mx+b$ ….1

where $m$ is the slope of the line and $b$ is the y-intercept.

Finding $b$:

The y-intercept of the line is (0,1) so $b=1.$

Finding $m$:

The slope of the line is the ration of the change of $y$ over the change in $x$ between any two points on the line.To find the slope between the points (0,1) and (4,-1)

  $\begin{array}{c}\text{slope=change}\text{in}y/\text{change}\text{in}x.\\ m=(y_{2-}{y}_1)/(x_2-x_1).\\ m=(-1-1)/(4-0).\\ m=-2/4.\\ m=-1/2.\end{array}$

Substituting the $b=1$ and $m=-1/2$ in equation ,

  $y=-x/2+1.$ so,

The equation of the line passes through (0,1),(2,0) and (4,-1) in slope-intercept form is $y=-x/2+1.$