y = 6x - 9 that passes through the point (-1, 4)

Answer 1

OK, Mark is correct in the comments in that you haven't asked a question. But typically, this type of problem asks you to find a line that is either parallel to or perpendicular to y = 6x-9 and goes through (-1,4). That's the part of your question that's missing. I'll do both.

Parallel to y = 6x - 9:

A line parallel to y = 6x - 9 will have the same slope (6) but a different y-intercept. So it's equation so far is:

y = 6x + b

where b is the y-intercept. To find the value of b, plug in the given point (-1,4):

y = 6x + b

4 = 6(-1) + b

4 = -6 + b

Solve for b then plug the value into y = 6x + b. That will be the answer.

Perpendicular to y = 6x - 9:

A line that's perpendicular to y = 6x - 9 will have a slope of -1/6 ( the negative reciprocal of 6). So it's equation so far would be:

y = -(1/6)x + b

To find the y-intercept (b), plug in the given point (-1,4):

y = -(1/6)x + b

4 = -(1/6)(-1) + b

4 = (1/6) + b

Solve for b.