Q36. - Algebra 2

Question

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

 36. slope $\frac{3}{4}$, passes through $\left(-6,9\right)$

Step-by-Step Solution

Answer

The equation of the line is $y=\frac{3}{4}x+\frac{27}{2}$.

Step-1 – Apply the concept of slope-intercept form

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.

Step-2 –Compute the intercept

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 $\frac{27}{2}$.

Step-3 – Construct the equation

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