Question

A line has a slope of 3 and contains the point (−1, −8).

Which equations represent the line?

Choose ALL answers that are correct.

A.
−3x + y = −5

B.
3x + y = −5

C.
(y – 8) = 3(x − 1)

D.
(y + 8) = 3(x + 1)

Answer 1

A.
-3x + y = -5
y = 3x -5 (the number before x is the slope.)

So, A. so far works, because it has a slope of 3.

Now, plug in the coordinate (-1,-8)

-8 = 3(-1) - 5
-8 = -3 -5
-8 = -8

This means that A. is one of the answers!!!!!!!

B.
3x + y = -5
y = -3x - 5

This doesn't work because it doesn't have the same slope.
B. is NOT one of the answers.

C.
(y-8) = 3 (x-1)
y - 8 = 3x - 3
y = 3x + 5

So far, it does work because it has a slope of 3.
It is not the same equation as A's equation, so it doesn't work

D.
(y + 8) = 3(x + 1)
y + 8 = 3x + 3
y = 3x - 5

THIS IS THE SAME EQUATION AS A'S EQUATION SO WE KNOW IT IS CORRECT!!!!!
So, D. is also correct.

Answer: A and D.

Answer 2

Simplest way to do this?:
Slope intercept form is y = mx+b where m is the slope, and b is the y intercept.
That means that our equation HAS to have y = 3x as the first part because it's the slope.
Now to find 'b'.
To find b there's two methods, and I'll be telling you both.
You can either plug (-1,-8) into the equation of y = 3x + b, or just add 3 to the -8 because you're basically trying to find the y intercept, which is at x = 0, which is just 1 unit away from -1,-8. And because you're increasing by intervals of 3 between each x unit, you just add 3 to the y value, and you have -5.

If you plug it in: -8 = -3 +b you'll get the same thing. b = -5
In this case answer choices A and D would be right.

Hope I helped :)