Answer:
A. y=2x-9
B. [tex]y=-\frac{1}{2}x+1[/tex]
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.
[tex]y-y_1 = m(x-x_1)\\y--1=2(x-4)\\y+1=2(x-4)\\y+1=2x-8\\y=2x-9[/tex]
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.
[tex]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[/tex]
