# Writing slope-intercept equations

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 -intercept and another point

Let's write the equation of the line that passes through the points and in slope-intercept form.

Recall that in the general slope-intercept equation , the slope is given by and the -intercept is given by .

### Finding

The -intercept of the line is , so we know that .

### Finding

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

Therefore, this is the slope between the points and :

**In conclusion, the equation of the line is .**

## Check your understanding

## Writing equations from any two points

Let's write the equation of the line that passes through and in slope-intercept form.

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

*a little bit*more difficult, but we are not afraid of a challenge!### Finding

### Finding

We know that the line is of the form , but we still need to find . To do that, we substitute the point 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 .

**In conclusion, the equation of the line is .**