How do you do slope intercept form with matching graphs to the equations???

You break it up and do the part you understand first. I have no idea what you mean by "matching graphs to equations," but I do know about slope-intercept form.

Slope is rise over run. Run is horizontal distance, left to right. Run is always positive because we always go left to right. Rise is the vertical change in that same distance. A negative rise means it drops.

The equation of a line is y = mx where m is the slope. That line passes through the origin. If you want it to pass through some point (a, b) you subtract the coordinates like this: y - b = m(x - a). That is the point-slope form, and you can rewrite it in other forms if it is convenient. You may do this with any point on the line. They all reduce to the same equation.

Ex. y = x - 3 Compare that to y = mx + b. The slope is m=1 and the intercept is -3. That means when y=0 then the graph intercepts the y axis at y=-3. Like this: www.wolframalpha.com/input/?i=plot+y+%3D+x+-+3

If you start with the graph then you can work backwards to get to the equation.