Chapter 8.5, Problem 21WE

To determine

To find: The equation in slope intercept form of the given line.

Answer to Problem 21WE

The equation in slope intercept form of the given lineis $y=-x+7$ .

Explanation of Solution

Given information:

The points through the line passes is $\left(8,1\right),\left(1,8\right)$ .

Calculation:

The slope of the line is,

  $\begin{array}{c}m=\frac{8-1}{1-8}\\ =\frac{7}{-7}\\ =-1\end{array}$

The slope intercept form is,

  $y=mx+c$

Here, the slope is $m$ and $y$ intercept is $c$ .

Substitute the values in above equation.

  $y=-x+c$.............(1)

Substitute the values of point through which the line is passing in above equation.

  $\begin{array}{l}1=-1\left(8\right)+c\\ 1=-8+c\\ c=7\end{array}$

Substitute the value in equation (1).

  $y=-x+7$