## Point Slope Form Lesson

### Definition of Point Slope Form

Point slope form is a way of representing the equation of a line passing through a point. **We can use it if we know any point along a line and the line's slope.** Point slope form is given as:

**y - y _{1} = m(x - x_{1})**

Where *(x _{1}, y_{1})* is a point along the line, and

*m*is the slope of the line.

INTRODUCING

### Point Slope to Slope Intercept Form

We can convert point slope form to slope intercept form with some simple algebraic manipulation. Here's the how to do it:

- Use the distributive property to multiply
*m*through the quantity of*(x - x*. We now have y - y_{1})_{1}= mx - mx_{1}. - Add y
_{1}to both sides of the equation. We now have y = mx - mx_{1}+ y_{1}. - Plugging in the coordinates
*x*and_{1}*y*and simplifying/combining terms gives us slope intercept form_{1}*y = mx + b*.

### Point Slope Form Practice Problems

Let's go through a couple of examples together to practice using point slope form.

#### Practice Problem 1

A line passes through (1, 2) and has a slope of 5. Write the equation of the line in point slope form.

Solution:

- We have a point and the slope, let's plug them into the formula.

y - 2 = 5(x - 1) **The equation of the line is****y - 2 = 5(x - 1).**

#### Practice Problem 2

A line passes through points (2, 4) and (8, 16). Write the equation of the line in point slope form.

Solution:

- First we must find the slope.

m =^{(y2 - y1)}⁄_{(x2 - x1)}

m =^{(16 - 4)}⁄_{(8 - 2)}=^{12}/_{6}= 2 - We will use the first given point with the slope we just found to get our point slope form equation.

y - 4 = 2(x - 2) **The equation of the line is y - 4 = 2(x - 2).**