# How do you write the equation in slope intercept form given (1,4) and (2,-5)?

##### 2 Answers
May 26, 2017

$y = - 9 x + 13$

#### Explanation:

Let's find the slope for $y = \textcolor{red}{m} x + b$, using $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$\frac{- 5 - 4}{2 - 1}$ gives us $- \frac{9}{1}$ for $m$

Now we need to find $b$, which is the $y$-intercept. That means, the value of $y$ when $x = 0$

To find that, let's us the point-slope formula again:

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ with (0,?) and $\left(1 , 4\right)$

(? - 4)/(0 - 1)
Now what? Well, we already know what the slope is. It's $- \frac{9}{1}$. Now we can solve!

(? - 4)/(0 - 1)=-9/1

(?-4)/-1=-9

multiply by $- 1$ on both sides

?-4=9

add $4$ on both sides

?=13

Now we have our $y$-intercept. It's $13$!

$y = - 9 x + 13$

Let's graph our equation and make sure it goes through the points $\left(2 , - 5\right)$ and $\left(1 , 4\right)$:

graph{y=-9x+13}
It does! We were right

May 26, 2017

$y = - 9 x + 13$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b. the y-intercept.

$\text{to calculate m use the "color(blue)"gradient formula}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
$\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) \text{ are 2 coordinate points}$

$\text{the points are } \left({x}_{1} , {y}_{1}\right) = \left(1 , 4\right) , \left({x}_{2} , {y}_{2}\right) = \left(2 , - 5\right)$

$\Rightarrow m = \frac{- 5 - 4}{2 - 1} = \frac{- 9}{1} = - 9$

$\Rightarrow y = - 9 x + b \leftarrow \text{ is the partial equation}$

$\text{to find b, substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using } \left(1 , 4\right)$

$4 = - 9 + b \Rightarrow b = 13$

$\Rightarrow y = - 9 x + 13 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$