# How do you write an equation given point (-2,3) slope -1?

Nov 12, 2016

$y = - 1 x + 1$

#### Explanation:

We can use the point-slope form of the equation to plug in values and solve for the equation.

use the slope of $- 1$ and the point of $\left(- 2 , 3\right)$

$m = - 1$
${x}_{1} = - 2$
${y}_{1} = 3$

The point-slope formula equation is

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

plug in the values

$y - 3 = - 1 \left(x - \left(- 2\right)\right)$ simplify the signs

$y - 3 = - 1 \left(x + 2\right)$ distribute the $- 1$

$y - 3 = - 1 x - 2$ use additive inverse to isolate the $y$

$y \cancel{- 3} \cancel{+ 3} = - 1 x - 2 + 3$ simplify

$y = - 1 x + 1$

Nov 12, 2016

Point-slope form: $y - 3 = - \left(x + 2\right)$

Y-intercept form: $y = - x + 1$

#### Explanation:

Use the point-slope equation: $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $\left({x}_{1} , {y}_{1}\right)$ is the given point $\left(- 2 , 3\right)$, and $m$ is the slope $- 1$.

Plug the numbers into the equation.

$y - 3 = - 1 \left(x - \left(- 2\right)\right)$

Simplify.

$y - 3 = - \left(x + 2\right)$

Solve for $y$ to get the slope-intercept form $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept.

Add $3$ to both sides.

$y = - x - 2 + 3$

Simplify.

$y = - x + 1$,

where $m = - 1$ and $b = 1$.

graph{y=-x+1 [-10, 10, -5, 5]}