Question

What is the y-intercept of the line perpendicular to the line y = four thirdsx + 1 that includes the point (4, 1)?

Answer 1

Answer:

(C)4

Step-by-step explanation:

Given the line: $y=\dfrac43 x+1$

The gradient of the line, $m=\dfrac43$

A line perpendicular to the given line will have a gradient, $m=-\dfrac34$ (by definition of perpendicularity).

Therefore, a perpendicular line that passes through the point (4,1) is:

$y-y_1=m(x-x_1)\\y-1=-\dfrac34(x-4)\\y-1=-\dfrac34x+3\\y=-\dfrac34x+3+1\\y=-\dfrac34x+4$

Comparing with the slope-intercept form y=mx+x, the slope of the perpendicular line, b=4.