Point-Slope Form

How to write and graph a linear equation in point-slope form: formula, 3 examples, and their solutions.

Formula

Formula

The linear equation in point-slope form is
y = m(x - x1) + y1.

m: Slope of the line
(x1, y1): Point on the line

Example 1

Example

Solution

The slope is 2.
And the point on the line is (1, 2).

Then the linear equation in point-slope form is
y = 3(x - 1) + 2.

Change the linear equation to slope-intercept form.

Then y = 3x - 1

So y = 3x - 1 is the answer.

Graph

This is the graph of the linear equation
y = 3(x - 1) + 2.

The slope is 3.
And the line passes through (1, 2).

Example 2

Example

Solution

To see the point part clearly,
change +4 to -(-4).

Then y = -2(x - (-4)) + 1.
This is in point-slope form.

The slope is -2.
And the line passes through (-4, 1).

See y = -2(x - (-4)) + 1.
The line passes through (-4, 1).

So draw the point (-4, 1)
on the coordinate plane.

See y = -2(x - (-4)) + 1 again.

The slope is -2. (= -2/1)

So move 1 unit to the right
and move 2 units downward.

Mark this endpoint.

Draw a line that passes through
(-4, 1) and the marked endpoint.

This is the graph of the linear equation
y = -2(x + 4) + 1.

Example 3

Example

The slope is not given.

So, from the given points (2, 1) and (5, 4),
find the slope of the line.

Solution

Draw a line that passes through (2, 1) and (5, 4).

Find the slope of the line.

The change of x is 5 - 2 = 3.
The change of y is 4 - 1 = 3.

So the slope is
m = 3/3 = 1.

The slope of the line is 1.
And the line passes through (2, 1).

Then the linear equation in point-slope form is
y = 1(x - 2) + 1.

You can also use the other point (5, 4).
You'll get the same answer.

Write the linear equation in slope-intercept form.
Then y = x - 1.

So y = x - 1 is the answer.