Answer:
The equation of the line:
[tex]y=\frac{3}{2}x+9[/tex]
Step-by-step explanation:
Given
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = -2/3
perpendicular to m = -1/m
[tex]=-\frac{1}{\left(\frac{-2}{3}\right)}=\frac{3}{2}[/tex]
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 3/2 and the point (-4, 3)
[tex]y-3=\frac{3}{2}\left(x-\left(-4\right)\right)[/tex]
[tex]y-3=\frac{3}{2}\left(x+4\right)[/tex]
Add 3 to both sides
[tex]y-3+3=\frac{3}{2}\left(x+4\right)+3[/tex]
[tex]y=\frac{3}{2}x+9[/tex]
Thus, the equation of the line:
[tex]y=\frac{3}{2}x+9[/tex]
