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Point Slope Form: Definition, Equation & Example

Instructor: Miriam Snare

Miriam has taught middle- and high-school math for over 10 years and has a master's degree in Curriculum and Instruction.

In this lesson, you will learn the definition and formula for writing the equation of a line in point-slope form. Then, we will look at a couple of examples. At the end, you will be able to test your knowledge with a quiz.

Definition

Using point-slope form means that you're supposed to write the equation of a line from knowing its slope and any point on the line. To visualize what's happening in this kind of a problem, let's imagine throwing a tennis ball onto a roof. The location where the ball hits the roof is the point you will use in the calculation. The steepness of the roof is the slope. The point-slope formula gives you an equation that describes the straight path that the tennis ball rolls down the roof.

Equation

The formula to find the equation of a line in point-slope form is:

y - y1 = m(x - x1)

To use this formula, you will substitute the coordinates of the known point for the x sub 1 and the y sub 1. You will also replace the m with the slope that you know. The x and y without the subscript 1 will remain variables in the formula. Usually, after substituting the values, the equation is written in slope-intercept form which is y = mx + b. To get from point-slope to slope-intercept form, you need to distribute and combine like terms (i.e. the same variables) so that only the y is on the left side of the equation. Let's look at some examples of how to do that.

Examples

Example #1: Find an equation of the line with a slope of 3 that passes through the point (2, 4).

The slope of 3 tells us to replace the m with 3. The point (2, 4) tells us that x sub 1 will be replaced with 2 and y sub 1 will be replaced with 4. Below you see the point-slope formula and below it, is the formula with the values filled in:

y - y1 = m(x - x1)

y - 4 = 3(x - 2)

After this, you usually put the equation into slope-intercept form by solving the equation for y. So, we distribute the 3 into the parentheses to get y - 4 = 3x - 6. Then, we have to add 4 to both sides of the equation to get y by itself. So, the final equation is y = 3x - 2.

Let's try another example.

Example #2: A line passes through the point (3, -5) and has a slope of 2/3. Find an equation of this line.

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