Question

What is the equation of the line that is parallel to the given line and passes through the point (12, -2)? A) y = -6/5x + 10 B) y= -6/5x + 12 C) y = -5/6x -10 D) y = 5/6x - 12

Answer 1

The answer is D I just took the test

Answer 2

D

Explanation:

Parallel lines are those that have the same slope, or coefficient of x.

Here, let's calculate the slope of the given line. Slope is the difference in the y-coordinates divided by the difference in the x-coordinates, so given the two coordinates (12, 6) and (0, -4):

slope = m = (-4 - 6) / (0 - 12) = -10 / (-12) = 10/12 = 5/6

So the slope is 5/6. That means the equation we want should also have a slope of 5/6. Already, we can eliminate A, B, and C, leaving D as our answer. But, let's check.

The equation of a line can be written as
`y-y_1=m(x-x_1)`, where m is the slope and
`(x_1,y_1)` is the coordinates of a given point.

Here, our slope is 5/6 and our given point is (12, -2). So plug these in:

`y-y_1=m(x-x_1)`

`y-(-2)=(5/6)(x-12)`

`y+2=(5)/(6) x-10`

`y=(5)/(6) x-12`

This matches D, so we know that it's the correct answer.

~ an aesthetics lover