How do you change an equation from point slope form to slope intercept form?

Answer 1

Start with point slope form
y - y1 = m(x - x1)

Distribute the slope m
y - y1 = mx - mx1

Add y1 to both sides
y = mx - mx1 + y1
y = mx + b

Example:
A line has a slope of 4 and passes the point (1,2). Write the equation of the line in slope-intercept form.

y - 2 = 4(x - 1)
y - 2 = 4x - 4
y = 4x-2

Answer 2

Example:

y = 3x + 2 (the slope-intercept form, y = mx + b, where slope = m = 3 = 3/1 and y-intercept = b = 2)

Since y-intercept is 2, we have the point (0, 2) where the line passes through.
Using the slope 3 and the point (0, 2) we can write the point-slope form of the equation of the line.

(y - y1) = m(x - x1)
(y - 0) = 3(x - 2)

Since the slope = changes in y/changes in x = rise/run = 3/1, then we can find another point on the line such that:

Let this point be (x1, y1), then
(x1, y1) = (x1 = 0 + 1, y1 = 2 + 3) = (1, 5)

Using the slope 3 and the point (1, 5) we can write the point-slope form of the equation of the line.

(y - y1) = m(x - x1)
(y - 5) = 3(x - 1)

Answer 3

The point slope form is (y - p) = m(x - q) where the coordinates of the given point are (p,q) and the slope is m.

Multiply out the brackets: y - p = mx - mq

Add p to both sides: y = mx - mq + p

that is y = mx + (p - mq)

This is in the slope intercept form with the [same] slope, m and the intercept is c = p - mq.