# Basic Algebra/Lines (Linear Functions)/Find the Equation of the Line Using Two Points

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## Vocabulary[edit]

## Lesson[edit]

You can find the y intercept(b) of a line by using "point slope" with a pair of cordinates.

-Find the slope (y_{2} - y_{1}) / (x_{2} - x_{1}) -Use one of the coordinates (points) and use this formula: y-y_{1}=m(x-x_{1}) -Then you end up with y=mx+b

## Example Problems[edit]

Find the y-intercept of the following coordinates:

(5,2) (3,6)

(7,6) (5,9)

(8,9) (5,2)

Example 1:

First find the slope m of between the two points:

m = (y2-y1) / (x2-x1)

m = (6-2) / (3-5)

m = -2

We know that the equation has the form y = mx + b, and we also know that this function passes both of the points, so let's use point #1 to find b:

point #1 (5,2)

2 = m(5) + b

2 = (-2)(5) + b

b = 12

Alternatively, we can use point #2 and get to the same result.

The line equation is:

y = -2x + 12