Write equation in slope-intercept form?

Question

has the same slope as 3x - y + 4 = 0 and contains the point (2, -3)

How do you turn a problem like the one above into slope-intercept form?

Answer 1

Step 1: Change the given equation to slope intercept form:
3x - y + 4 = 0

Add y to both sides:
3x - y + 4 + y = y
3x + 4 = y (slope-intercept form)

Step 2: Taking the slope intercept form equation, use the slope and the given point to define a new equation.
Slope = 3
Point = 2, -3
Slope = rise/run

Since for slope intercept you need to find the y-intercept (x = 0), take the negative value of x from your point (-2), and plug it as the run in your slope equation:
slope = rise / run
rise = slope * run = 3 * -2 = -6.

Thus, from point (2,-3), you run -2 and rise -6, giving you a y-intercept point of (0,-9).

Step 3: Given the slope and the y-intercept, write the new equation in slope intercept form:
y = = 3x - 9 (solution!)

Answer 2

So I'm guessing it's going to be something like y=3x + __

You're going to want to graph that line on paper, and think, "okay, so it intercepts with the other at 2,-3, so find that point and create the other line with the slope. Then you can find the y-intercept to complete the formula.

I'm just guesing however. I've never been asked to do questions like this. Anyone correct me if I'm totally wrong.