Answer:
Step-by-step explanation:
The a line that is perpendicular to the reference line will have a slope that is the negative inverse of the slope of the reference line. We'll look for a line that has the form y=mx+b, where m is the slope and b is the y-intercept. The reference line y=(4/3)x has a slope of (4/3) and a y-intercept of 0 (it crosses the y axis at x = 0).
The negative inverse the the slope (4/3) would be -(3/4).
The new line will be y = -(3/4)x + b.
To find point, use the given point and solve for b:
y = -(3/4)x + b
y = -(3/4)x + b for point (4,2)
2= -(3/4)(4) + b
2= -3 + b
b = 5
The equation of the perpendicualr line is y = -(3/4)x + 5
See attached graph.
