Question

Which of the following equations defines a line that is parallel to the line y=-4/3x-4 and passes through the point (3,-1)

Answer 1

Answer:

D.

Step-by-step explanation:

The given line is

$y=-\frac{4}{3}x-4$

Now, if the new line is parallel to the given one, that means it must have the same slope.

$m=-\frac{4}{3}$

We also know that the new line passes through point (3,-1).

Then, we use the point-slope formula to find the equation of the new line:

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

Therefore, the line that passes through (3,-1) and it's parallel to the given line is: $y=-\frac{4}{3}x+3$.

The image attached show these parallel lines.

Answer 2

Answer:

d

Step-by-step explanation:

given that your slop is -4/3, plug the (x,y) point in to the equation of y = -4x/3 +b

-1 = -4 + b , b = 3

y = -4x/3 + 3