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## Algebra basics (ASL)

### Course: Algebra basics (ASL) > Unit 4

Lesson 7: Writing slope-intercept equations (ASL)- Slope-intercept equation from graph
- Writing slope-intercept equations (ASL)
- Slope-intercept equation from graph
- Slope-intercept equation from slope & point
- Slope-intercept equation from two points
- Slope-intercept from two points
- Slope-intercept form problems
- Slope-intercept form review

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# Writing slope-intercept equations (ASL)

Learn how to find the slope-intercept equation of a line from two points on that line.

If you haven't read it yet, you might want to start with our introduction to slope-intercept form.

## Writing equations from y-intercept and another point

Let's write the equation of the line that passes through the points left parenthesis, 0, comma, 3, right parenthesis and left parenthesis, 2, comma, 7, right parenthesis in slope-intercept form.

Recall that in the general slope-intercept equation y, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #0d923f, b, end color #0d923f, the slope is given by start color #ed5fa6, m, end color #ed5fa6 and the y-intercept is given by start color #0d923f, b, end color #0d923f.

### Finding start color #0d923f, b, end color #0d923f

The y-intercept of the line is left parenthesis, 0, comma, start color #0d923f, 3, end color #0d923f, right parenthesis, so we know that start color #0d923f, b, end color #0d923f, equals, start color #0d923f, 3, end color #0d923f.

### Finding start color #ed5fa6, m, end color #ed5fa6

Recall that the slope of a line is the ratio of the change in y over the change in x between any two points on the line:

Therefore, this is the slope between the points left parenthesis, 0, comma, 3, right parenthesis and left parenthesis, 2, comma, 7, right parenthesis:

**In conclusion, the equation of the line is y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, start color #0d923f, plus, 3, end color #0d923f.**

## Check your understanding

## Writing equations from any two points

Let's write the equation of the line that passes through left parenthesis, 2, comma, 5, right parenthesis and left parenthesis, 4, comma, 9, right parenthesis in slope-intercept form.

Note that we are not given the y-intercept of the line. This makes things

*a little bit*more difficult, but we are not afraid of a challenge!### Finding start color #ed5fa6, m, end color #ed5fa6

### Finding start color #0d923f, b, end color #0d923f

We know that the line is of the form y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, plus, start color #0d923f, b, end color #0d923f, but we still need to find start color #0d923f, b, end color #0d923f. To do that, we substitute the point left parenthesis, 2, comma, 5, right parenthesis into the equation.

Because any point on a line must satisfy that line’s equation, we get an equation that we can solve to find start color #0d923f, b, end color #0d923f.

**In conclusion, the equation of the line is y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, start color #0d923f, plus, 1, end color #0d923f.**

## Check your understanding

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