91Ó°ÊÓ

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

The y-intercept of a graph is when the x-coordinate is 0. The point where the graph of the equation cuts the y-axis.

It is provided that line passes through the point $\left(-6,9\right)$with slope $m=\frac{3}{4}$.

So, to find the y-intercept that is value of c, follow the step provided below.

Substitute x as $-6$, y as 9 and m as \[\frac{3}{4}\] in the equation \[y=mx+c\].

$\begin{array}{c}9=\frac{3}{4}\left(−6\right)+c\\ 9=−\frac{9}{2}+c\\ 9+\frac{9}{2}=c\\ \frac{27}{2}=c\end{array}$

Therefore, y-intercept is $\frac{27}{2}$.

Recall the equation of line in slope-intercept form that is $y=mx+c$.

Where m is the slope and c is the intercept of y-axis.

Replace m by $\frac{3}{4}$ and c by $\frac{27}{2}$ to obtain equation of line in slope-intercept form.

$y=\frac{3}{4}x+\frac{27}{2}$

Hence, equation of line with slope $\frac{3}{4}$ and passing through the point $\left(-6,9\right)$ is $y=\frac{3}{4}x+\frac{27}{2}$.