Chapter 13.6, Problem 17WE

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 17WE

The slope is $-\frac{2}{3}$ and the y-intercept is $-4$ .

Explanation of Solution

Given information:Line: $y=-\frac{2}{3}x-4$ .

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

Calculation:

Comparing the line $y=-\frac{2}{3}x-4$ with equation $y=mx+b$ :

The slope of line, $m=-\frac{2}{3}$ and the $y\text{-intercept, }b=-4$

Since, $y\text{-intercept is }-4$

So, one point is $(x_1,y_1)\equiv (0,-4)$

For one more point, using $m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}$ :

Let taking $x_2=-3$ , then

  $\begin{array}{l}\frac{y_2-(-4)}{-3-0}=-\frac{2}{3}\\ \Rightarrow y_2+4=-\frac{2}{3}\times (-3)\\ \Rightarrow y_2=2-4\\ \Rightarrow y_2=-2\end{array}$

So, second point is $(x_2,y_2)\equiv (-3,-2)$

Hence, the slope is $-\frac{2}{3}$ and the y-intercept is $-4$ .

Graph: