How do you use the y intercept and slope of a line to graph it?

Here is an example. y = 2x + 3; that is, the slope is 2, and the y-intercept is 3.

Start with the y-intercept. Plot the point (0, 2).

Now, for the slope: a slope of 2 means that every time you go 1 to the right, you have to go 2 up. Thus, the next point to the right (if you use plotting paper, and one square for each number) would be 1, 4. That is, if you add 1 to the x-coordinate, you have to add 2 to the y-coordinate. After that, once again adding 1 and 2, you get 2, 6. Plot these points, and draw a line through them.

Similarly, if you go to the left, for every unit you go to the left you have to go 2 units down.

2, in this case, is the slope; for other slopes, you just have to change the numbers.