Question

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.

y = –Three-fourthsx + 1
3x − 4y = −4
4x − 3y = −3
y – 2 = –Three-fourths(x – 4)
y + 2 = Three-fourths(x + 4)

Answer 1

the second one (3x − 4y = −4), and the last one (y + 2 = Three-fourths(x + 4)

Explanation:

First, the equation given is equal to y = (3/4)x - 7/4

To find the equation of a line that is parallel to that, we need the same slope but different y-intercept.

y = (3/4)x + b

Now substitute to given point, (-4, -2), into the equation.

-2 = (3/4 × -4) + b

-2 = - 3 + b

b = 1

The equation is

y = 3/4 x + 1

So in the options,

the second one (3x − 4y = −4), and the last one (y + 2 = Three-fourths(x + 4) are the answers.