# How do you write an equation in slope intercept form given (2, 4) and (1, –3)?

Nov 21, 2017

$y = 7 x - 10$

See the explanation for the process.

#### Explanation:

First determine the slope using the slope formula:

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

where:

$m$ is the slope, $\left({x}_{1} , {y}_{1}\right)$ is one point, and $\left({x}_{2} , {y}_{2}\right)$ is the second point.

Point 1: $\left(2 , 4\right)$

Point 2: $\left(1 , - 3\right)$

Plug the known values into the formula:

$m = \frac{- 3 - 4}{1 - 2}$

Simplify.

$m = \frac{- 7}{- 1}$ $\leftarrow$ two negatives make a positive

$m = 7$

Now determine the linear equation using the point-slope form:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$,

where ${y}_{1}$ and ${x}_{1}$ are a point, and $m = 7$

We can use one of the points from determining the slope. I'm going to use Point 1: $\left(2 , 4\right)$.

Plug in the given point and slope.

$y - 4 = 7 \left(x - 2\right)$ $\leftarrow$ point-slope form

We can solve the point-slope form for $y$, which will give us the slope-intercept from:

$y = m x + b$,

where:

$m$ is the slope and $b$ is the y-intercept.

$y - 4 = 7 \left(x - 2\right)$

Expand.

$y - 4 = 7 x - 14$

Add $4$ to both sides.

$y = 7 x - 14 + 4$

Simplify.

$y = 7 x - 10$, $\leftarrow$ slope-intercept form

where the slope $\left(m\right)$ is $7$ and the y-intercept $\left(b\right)$ is $- 10$.