# How do you write an equation in standard form given point (-2,5) and slope 1?

May 7, 2017

y = x+7

#### Explanation:

• Use the formula y=mx+c
c= y intercept

• Substitute y,m and x in equation to find c
$5 = 1 \cdot - 2 + c$
$5 = - 2 + c$
7=c

• Replace m and c with numbers found
Therefore equation is y = x + 7

May 7, 2017

$x - y = - 7$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where A is a positive integer and B, C are integers}$

$\text{begin by expressing the equation in "color(blue)"point-slope form}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

$\text{here " m=1" and } \left({x}_{1} , {y}_{1}\right) = \left(- 2 , 5\right)$

$y - 5 = 1 \left(x - \left(- 2\right)\right)$

$\Rightarrow y - 5 = x + 2 \leftarrow \textcolor{red}{\text{ in point-slope form}}$

$\text{subtract y from both sides}$

$\cancel{y} \cancel{- y} - 5 = x + 2 - y$

$\Rightarrow - 5 = x + 2 - y$

$\text{subtract 2 from both sides}$

$- 5 - 2 = x \cancel{+ 2} \cancel{- 2} - y$

$\Rightarrow - 7 = x - y \text{ or }$

$x - y = - 7 \leftarrow \textcolor{red}{\text{ in standard form}}$