Q67. - Algebra 2

Question

Write an equation in slope-intercept form for the line that satisfies the following set of conditions. 

 

Slope $-\frac{4}{3}$ passes through $\left(6,-8\right)$.

Step-by-Step Solution

Answer

The solution is $3y=-4x$.

Step 1- Consider the set of conditions.

Consider the slope $m=-\frac{4}{3}$ passes through the points $\left(x,y\right)=\left(6,-8\right)$.

Step 2- Step description.

The slope intercept form is given by the formula $y=mx+b$, where $m$ is the slope.

Step 3- Step description.

Substitute the value of $m$ and the set of points in the slope intercept equation as follows:

 

$\begin{array}{l}y=mx+b\\ -8=-\frac{4}{3}\left(6\right)+b\\ -8=-8+b\\ b=-8+8\\ b=0\end{array}$

 

Now substitute the value of slope and $b$ in the slope intercept form as follows:

 

$\begin{array}{l}y=mx+b\\ y=-\frac{4}{3}\left(x\right)+0\\ 3y=-4x\end{array}$.

 

Thus, the slope intercept form is $3y=-4x$.