Chapter 1.1, Problem 59E

To determine

Find an equation of the line that passes through the points.Also,use the slope − intercept form (if possible).If not possible,explain why and use the general form.Also,use a graphing utility to graph the line (if possible).

Answer to Problem 59E

The equation of the line that passes through the points is $x=-8$ .

Explanation of Solution

Given:

It is given in the question that the two coordinates are $(-8,1),(-8,7)$ .

Concept Used:

In this ,use the conept of slope equation and the slope intersept form and the formula used is $m=\frac{y_2-y_1}{x_2-x_1}$ and $y=mx+b$ .

Calculation: Use the slope formula to solve for the slope,

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-1}{-8-(-8)}=\frac{6}{-8+8}=\frac{6}{0}=\infty$

Since the slope is undefined,the line is a vertical line.If the points,noth points have an x − value of $-8$ ,this is another way to tell that the line is vertical.

Since all points on this line have an x − value of $-8$ ,

The equation of the line is $x=-8$ .

The graph will be ,

  

Conclusion:

The equation will be $x=-8$ .