Question

Consider the point P = (4,-1) and the line L, given by the equation y=2x+3.

Answer 1

Answer:

A. y=2x-9

B. $y=-\frac{1}{2}x+1$

Step-by-step explanation:

A. Parallel lines have the same slope. That means the line y=2x+3 has the same slope as any line parallel to it. So the slope is 2.

Using m=2, substitute it and (4,-1) into the point slope form and simplify to find the y-intercept.

$y-y_1 = m(x-x_1)\\y--1=2(x-4)\\y+1=2(x-4)\\y+1=2x-8\\y=2x-9$

B. Perpendicular lines have slopes which are negative reciprocals of each other. The slope of the line y=2x+3 is 2. The slope perpendicular to it is -1/2.

Using m=-1/2, substitute it and (4,-1) into the point slope form and simplify to find the y-intercept.

$y-y_1 = m(x-x_1)\\y--1=-\frac{1}{2}(x-4)\\y+1=-\frac{1}{2}(x-4)\\y+1=-\frac{1}{2}x+2\\y=-\frac{1}{2}x+1$