Once you have a point and a slope, then using the point slope formula, you can find the line generated by this info. Point-slope form is the following equation:

y-y1 = m*(x-x1)

That probably looks a mess, but what it says is that given a point (x1,y1) and a slope m, the line that they form is given by y = y1 + m*(x-x1).

For example: let's say you're given the points (2,1) and (4,9). We want to find the equation of the line that goes between them. First we find it's slope: m = (9-1)/(4-2)=4 (it's just the difference of the y coordinates over the difference in the x coordinates).

So we have the slope m=4, and two points, (2,1) and (4,9). Let's pick just one of those points, (2,1), and plug this into point-slope form.

y-1= 4*(x-2)

Solving for y, we get y = 4x-7. Notice that if we plug x = 2 into that equation, we get 1, and if we plug x=4, we get y=9. So both points lie on that line, which is exactly what we wanted.

Note: It doesn't matter which given point I choose. If I instead chose (4,9), then the point slope formula gives