Question

How to find an equation when you have a point on a graph and a slope??

Answer 1

the form of the equation that most students seem to learn is y = mx + b, where m is the slope and b is the y-intercept.

I will use a specific example.
suppose you know the slope is -2/3 and the given point is (9,1)

so y = -2/3 m + b
but (9,1) lies on it, so
1 = (-2/3)(9) + b
1 = -6 + b
b = 7

so the equation is y = -2/3 x + 7

there are other ways:
you could say (y-1)/(x-9) = -2/3, cross-multply
3y - 3 = -2x + 18
2x + 3y = 21, this is the standard form

2x + 3y - 21 = 0 is called the general form

there are several other variations of these two methods