Chapter 1.1, Problem 57E

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 57E

The equation of the line that passes through the points is $y=\frac{-6}{5}x-\frac{18}{25}$ .

Explanation of Solution

Given:

It is given in the question that the two coordinates are $(-\frac{1}{10},-\frac{3}{5}),(\frac{9}{10},\frac{-9}{5})$ .

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,

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{(\frac{-3}{5})-(\frac{-9}{5})}{(\frac{-1}{10})-(\frac{9}{10})}=\frac{\frac{6}{5}}{-1}=\frac{-6}{5}$

Now,plug a point into the slope intercept form ro solve b.

  $\begin{array}{l}\frac{-3}{5}=-\frac{6}{5}(\frac{-1}{10})+b\\ -30=6+50b\\ b=\frac{-36}{50}=\frac{-18}{25}\end{array}$

Now,use the slope intersept form,

  $\begin{array}{l}y=mx+b\\ y=\frac{-6}{5}x-\frac{18}{25}\end{array}$

The graph will be ,

  

Conclusion:

The equation will be $y=\frac{-6}{5}x-\frac{18}{25}$ .