Chapter 5.3, Problem 6STP

What is an equation of the line that passes through (-8,2) and has slope $-\frac{3}{4}?$

What is the graph of the equation?

To determine

To find the equation and graph of a line that passes through given point and slope also given.

Answer to Problem 6STP

The equation of line is $y=-\frac{3}{4}x-4$ .

The graph of line is:

Explanation of Solution

Given information: We have given a coordinate $\left(-8,2\right)$ and slope of line $-\frac{3}{4}$ .

Formula Used: Point slope form $\left(y-y_1\right)=m\left(x-x_1\right)$ , where $(x_1,y_1)$ is a point on the line and m is the given slope of the line.

Solution: In order to find an equation of line we need to plug the given coordinate $\left(-8,2\right)$ for $(x_1,y_1)$ and slope of line $-\frac{3}{4}$ for m in point slope form $\left(y-y_1\right)=m\left(x-x_1\right)$ .

We get

$\left(y-2\right)=-\frac{3}{4}\left(x+8\right)$

Simplify and convert this equation into slope intercepts form $y=mx+b$ .

  $y-2=-\frac{3}{4}x-6$

Add 2 on both sides of the equation

$y-2+2=-\frac{3}{4}x-6+2$

$y=-\frac{3}{4}x-4$

So, the required equation of line is $y=-\frac{3}{4}x-4$ .

Now, plug the given coordinate $\left(-8,2\right)$ and the y-intercept (0,-4).

Join the points and draw a straight line.

Therefore, the graph of the line is: