Chapter 1.1, Problem 55E

To determine

Find an equation of the line that passes through the points.Also,use the slope − intersept 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 55E

The equation of the line that passes through the points is $y=-2x+4.5$ .

Explanation of Solution

Given:

It is given in the question that the two coordinates are $(2,\frac{1}{2}),(\frac{1}{2},\frac{5}{4})$ .

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,

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{\frac{1}{2}-2}{\frac{5}{4}-\frac{1}{2}}=\frac{\frac{-3}{2}}{\frac{3}{4}}=\frac{-3}{2}\times \frac{4}{3}=\frac{-12}{6}=-2$

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

  $\begin{array}{l}\frac{1}{2}=-2(2)+b\\ \frac{1}{2}=-4+b\\ \frac{1}{2}+4=b\\ b=4.5\end{array}$

Now,use the slope intersept form,

  $\begin{array}{l}y=mx+b\\ y=-2x+4.5\end{array}$

The graph will be ,

  

Conclusion:

The equation will be $y=-2x+4.5$ .