Question

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

Answer 1

Answer:

Option B and E

Step-by-step explanation:

A line is given as 3x - 4y = 7

We have to find the equation of a line parralel to the given line which passes through point (-4, -2).

Let the equation is y = mx + c

Line parallel to 3x - 4y = 7 will have same slope

3x - 4y = 7

-4y = 7 - 3x

4y = 3x - 7

y = $\frac{1}{4}$ (3x - 7 ) ≈ $\frac{3}{4}$x - $\frac{7}{4}$

So slope of the line will be m = $\frac{3}{4}$

Since the given line passes through (-4, -2)

So we put the values in y = mx + c to get the value of c.

-2 = $\frac{3}{4}$ (-4 ) + c

-2 = -30 +c

c = 3 - 2 = 1

Therefore, equation will be

y = $\frac{3}{4}$x + 1 ----------(1)

We further solve equation (1)

4y = 3x + 4

3x - 4y = -4 ---Option B

By solving the equation (1) in other way

y + 2 = $\frac{3}{4}$x + 1 + 2

$\frac{3}{4}$x + 3

y + 2 = $\frac{3}{4}$ (x+4)  --Option E

Option B and E are the answers.

Answer 2

You plug in the point into each equation to see if the answer comes out equal. Such as the first one, so you have y=-3/4x+1. So you plug in the -4 for the x then plug in the -2 for y. So you get -2=1.1875, as you see both sides don't add up. As you progress in Algebra I'm guessing that you're in, you'll progress as the year goes on. So your answers are 3x-4y=-4 and y+2=3/4(x+4).