Answer:
y = 3x/2-14
Step-by-step explanation:
We are given that the line is perpendicular to y = -2/3 and contains (4,-8).
Perpendicular Def.
[tex] \displaystyle \large{m_1m_2 = - 1}[/tex]
Both slopes multiply each others equal to -1.
Finding another slope that is perpendicular to -2/3, substitite m1 = -2/3 in.
[tex] \displaystyle \large{ - \frac{2}{3} m_2 = - 1}[/tex]
Multiply both sides by 3.
[tex] \displaystyle \large{ - \frac{2}{3} m_2( 3) = - 1(3)} \\ \displaystyle \large{ - 2 m_2= - 3} \\ \displaystyle \large{ m_2= \frac{3}{2} }[/tex]
Therefore, another slope that is perpendicular to -2/3 is 3/2.
Then rewrite in slope-intercept form.
Slope-Intercept
[tex] \displaystyle \large{y = mx + b}[/tex]
where m = slope and b = y-intercept; substitute m = 3/2 in.
[tex] \displaystyle \large{y = \frac{3}{2} x + b}[/tex]
Since the line contains (4,-8), substitute x = 4 and y = -8 in and solve for b.
[tex] \displaystyle \large{ - 8 = \frac{3}{2} (4) + b} \\ \displaystyle \large{ - 8 = 3(2)+ b} \\ \displaystyle \large{ - 8 = 6 + b} \\ \displaystyle \large{ - 8 - 6 = b} \\ \displaystyle \large{ - 14 = b}[/tex]
Therefore, b is -14; rewrite again in slope-intercept form.
Thus:-
[tex] \displaystyle \large{y = \frac{3}{2} x + b} \\ \displaystyle \large{y = \frac{3}{2} x - 14}[/tex]
