Answer:
[tex]y=\frac{2}{3}x-2[/tex] (in slope-intercept form)
Step-by-step explanation:
Slope intercept form of line is y = mx + b
The line y = -3/2 x - 7 has a slope of -3/2 and y-intercept of -7
Perpendicular line will have slope that is "negative reciprocal" of this.
So perpendicular line will have a slope = 2/3
Thus, we can write:
y = 2/3 x + b [perpendicular line equation]
To find b, we plug in -3 into x and -4 into y (point given) and find b:
[tex]y=\frac{2}{3}x+b\\-4=\frac{2}{3}(-3)+b\\-4=-2+b\\b=-2[/tex]
Thus, perpendicular line has equation: [tex]y=\frac{2}{3}x-2[/tex]
