Chapter 13.2, Problem 21PSC

To determine

To find: Whether the point $\left(12,-3\right)$ lie on the line whose slope is $-\frac{3}{4}$ and whose $y$ intercept is 5.

Answer to Problem 21PSC

No, the point $\left(12,-3\right)$ does not lie on the line.

Explanation of Solution

Given:

It is given that the point $\left(12,-3\right)$ lie on the line whose slope is $-\frac{3}{4}$ and whose $y$ intercept is 5.

Calculation:

The slope intercept form of line equation is $y=mx+b$ , where $m$ is slope and $b$ is y-intercept.

Substitute $-\frac{3}{4}$ for $m$ , and 5 for $b$ in the equation $y=mx+b$ .

  $y=-\frac{3}{4}x+5$

Substitute $12$ for $x$ , and $-3$ for $y$ in the equation $y=-\frac{3}{4}x+5$ to check whether the point lie on the line.

  $\begin{array}{c}-3=-\frac{3}{4}\left(12\right)+5\\ -3=-9+5\\ -3\ne -4\end{array}$

Therefore, no, the point $\left(12,-3\right)$ does not lie on the line.