Okay so slope-intercept form looks like:

y = mx + b

Where m is the slope of the graph and b is the y-intercept (hence the name slope-intercept).

The y intercept is where the graph crosses the y-axis. Because it lies on the y-axis, at this point, x must equal 0. So the point will be (0, b) where it crosses.

The slope of the graph is how many y the graph goes up for each x. This is generally stated as rise/run. If the slope is negative, the graph goes down from left to right, positive goes up from left to right.

For example, if m = 3/5 for every 3 y the graph goes up, it goes 5 x to the right.

How do you figure out y?

Well, if you know the x-coordinate of the point, say you were given (3, y) and told to find y for the equation:

y = (4/3)x + 5

You just plug in the 3, since that is what x is equal to at the y you want, and solve the equation. In this example, it would look like this:

y = (4/3)(3) + 5

y = 4 + 5

y = 9

So we would conclude that the point when x is equal to 3 is (3, 9).

Let's say the reverse is true, you are given some y value and told to find x. For this example, we'll say that you must find x when y = 12 for the equation:

y = -2x - 4

Well, we know that y = 12, so we just substitute 12 for y and solve for x, like so:

12 = -2x -4

16 = -2x

-8 = x

So when y = 12, x = -8. If you were asked to give the point, this would be at the point (-8, 12)

If you are asked to find if a given point is on the line, just plug in the x and y and see if it's equal. An example would be:

Is the point (4, 7) on the line y = -(1/2)x + 10?

To check:

7 = -(1/2)(4) + 10

7 = -2 + 10

7 = 8

7 doesn't equal 8, so this point is not on the line.

There is another form for the equation of a line that looks like this:

y - k = m(x - h)

This gives you the slope m and some point on the line (h, k). While slightly less useful for finding the y-intercept of the graph just by looking at it, you can still substitute 0 for x and find it with a little bit of arithmetic.

This form, however, is a lot easier to use if you're told to write an equation of a line that passes through a point. Even if you're required to use slope-intercept form, you can still substitute the terms and rearrange it to make it slope-intercept fairly easily.

Other than those things, if you had any specific issues or examples with which you have trouble, I'd be happy to help, or if you need me to clarify something I've said here.