Chapter 13.6, Problem 18WE

To determine

To find:Slope and y-intercept of each line. Plot the y-intercept. Then using the slope, plot one more point. Finally graph the line.

Answer to Problem 18WE

The slope is $\frac{5}{3}$ and the y-intercept is $-2$ .

Explanation of Solution

Given information:Line: $y=\frac{5}{3}x-2$ .

Concept Used:A line with the equation $y=mx+b$ has slope $m$ and $y\text{-intercept }b$ .

Calculation:

Comparing the line $y=\frac{5}{3}x-2$ with equation $y=mx+b$ :

The slope of line, $m=\frac{5}{3}$ and the $y\text{-intercept, }b=-2$

Since, $y\text{-intercept is }-2$

So, one point is $(x_1,y_1)\equiv (0,-2)$

For one more point, using $m=\frac{y_2-y_1}{x_2-x_1}=\frac{5}{3}$ :

Let taking $x_2=3$ , then

  $\begin{array}{l}\frac{y_2-(-2)}{3-0}=\frac{5}{3}\\ \Rightarrow y_2+2=\frac{5}{3}\times 3\\ \Rightarrow y_2=5-2\\ \Rightarrow y_2=3\end{array}$

So, second point is $(x_2,y_2)\equiv (3,3)$

Hence, the slope is $\frac{5}{3}$ and the y-intercept is $-2$ .

Graph: