Algebra

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# Point Slope Form

## 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.

### 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:

1. Use the distributive property to multiply *m* through the quantity of *(x – x _{1})*. We now have y – y

_{1}= mx – mx

_{1}.

2. Add y

_{1}to both sides of the equation. We now have y = mx – mx

_{1}+ y

_{1}.

3. 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

**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).**

**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).**