Chapter 1.1, Problem 56E

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 56E

The equation of the line that passes through the points is $y=\frac{-1}{3}x+\frac{4}{3}$ .

Explanation of Solution

Given:

It is given in the question that the two coordinates are $(1,1),(6,\frac{-2}{3})$ .

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,

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(\frac{-2}{3})}{1-6}=\frac{\frac{5}{3}}{-5}=\frac{-1}{3}$

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

  $\begin{array}{l}1=-\frac{1}{3}(1)+b\\ 3=-1+3b\\ b=\frac{4}{3}\end{array}$

Now,use the slope intersept form,

  $\begin{array}{l}y=mx+b\\ y=\frac{-1}{3}x+\frac{4}{3}\end{array}$

The graph will be ,

  

Conclusion:

The equation will be $y=\frac{-1}{3}x+\frac{4}{3}$ .