Question

I need the answers to these questions quickly, please:

Choose the equation of the line passing through the point (-4, -2)and parallel to y = 1/4 x + 2.

y = 1/4 x - 1
y = 4x - 1
y = 1/4 x - 3
y = 4x - 3

Choose the equation of the line passing through the point (-1, 7)and perpendicular to y = -1/4x - 5.

y = 4x + 3
y = -4x - 11
y = -4x - 3
y = 4x + 11

Answer 1

1. y = 1/4 x - 1
2. y = 4x + 11

Explanation:

It is probably easiest to identify the required slope so you can eliminate the bogus answers, then try the point in the remaining equations to see what works.

1. Parallel lines have the same slope. A line parallel to a line with slope 1/4 will also have slope 1/4, eliminating the 2nd and 4th answer choices.

Trying the point in the first answer choice, we have ...

-2 = (1/4)(-4) -1 . . . . true . . . . . y = 1/4x -1 is the correct equation

__

2. Perpendicular lines have slopes that are the negative reciprocal of each other. -1/(-1/4) = 4, eliminating the 2nd and 3rd choices.

Trying the point in the first answer choice, we have ...

7 = 4(-1) +3 . . . . . . false

The last answer choice gives ...

7 = 4(-1) +11 . . . . . . true . . . . . . y = 4x +11 is the correct equation