# Write an Equation Given Two Points

## Key Questions

• Slope Formula

The slope formula of the line passing through the points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ can be found by:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

So to find the slope of a line segment joining the points ( 2, - 5) and (- 2, 4).

First, label the points as ${x}_{1}$ = 2, ${y}_{1}$ = - 5, ${x}_{2}$ = -2 and ${y}_{2}$ = 4

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ = $\frac{4 - - 5}{- 2 - 2}$ = $\frac{9}{- 4}$ = $\frac{- 9}{4}$

So, the slope ($m$) = -9/4.

• No, it does not as long as the point is on the line. You will end up with the same value for the $y$-intercept.

I hope that this was helpful.

• If the slope of a line is undefined, then the line is a vertical line, so it cannot be written in slope-intercept form, but it can be written in the form: $x = a$, where $a$ is a constant.

Example

If the line has an undefined slope and passes through the point $\left(2 , 3\right)$, then the equation of the line is $x = 2$.

I hope that this was helpful.

Use the differences in the y and x values to find the slope then substitute the values of one point into the equation to find b the y intercept.

#### Explanation:

Slope = $\frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}} = m$

By putting the x and y values for the two points into the slope equation the value for m can be found.

The equation of a line in the slope intercept form is

$y = m x + b$

After finding m using the slope equation substitute one set of point values for y and x. This leaves b as the only unknown. Slope the resulting equation for b.