Suppose we want to find the equation of a line that passes through the point (3, -4) and has a slope of 6. How do we find the equation?

There are two methods. You can use the equation y - y1 = m(x - x1) where (x1, y1) is (3, -4) and m = 6.

Substitute the values into the equation to get

y - (-4) = 6(x - 3)

y + 4 = 6x - 18

y = 6x - 22

We can also use the equation y = mx + b, subtitute the values for x, y and m into the equation and solve for b.

-4 = 6(3) + b

-4 = 18 + b

-22 = b

Now substitute 6 for m and -22 for b into y = mx + b to get

y = 6x - 22.