Chapter 1, Problem 10CT

To determine

The slope-intercept form of the line containing the point $\left(3,-4\right)$ and having slope $-2$, and graph the line.

Answer to Problem 10CT

Solution:

The slope-intercept form of the line is $y=-2x+2$ .

The graph of the line $y=-2x+2$ is:

  

Explanation of Solution

Given information:

The point is $\left(3,-4\right)$, and the slope of line is $-2$ .

Point-slope form of an equation of a line is $y-y_1=m\left(x-x_1\right)$ .

Here, $m=-2$, and $\left(x_1,y_1\right)=\left(3,-4\right)$ .

By substituting values of $m,x_1$ and $y_1$ in $y-y_1=m\left(x-x_1\right)$, it gives

  $y-\left(-4\right)=-2\left(x-3\right)$ .

By simplifying,

  $\Rightarrow y+4=-2x+6$ .

  $\Rightarrow y=-2x+6-4$ .

  $\Rightarrow y=-2x+6-4$ .

  $\Rightarrow y=-2x+2$ .

So, the slope-intercept form of the line containing point $\left(3,-4\right)$, and having slope $-2$, is $y=-2x+2$ .

The graph of the equation of line $y=-2x+2$ is: