How do you write an equation with slope -2 that passes through the point (1, 5) ?

Oct 3, 2015

$\left(y - 5\right) = \left(- 2\right) \left(x - 1\right)$ (point-slope form), or
$y = - 2 x + 7$$\textcolor{w h i t e}{\text{XXXXXX}}$ (slope-intercept form), or
$2 x + y = 7$$\textcolor{w h i t e}{\text{XXXXXXXX}}$ (standard form)

Explanation:

Point-slope form of a line with slope $m$ through the point $\left(\hat{x} , \hat{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

For the given values:
$\textcolor{w h i t e}{\text{XXX}} \left(y - 5\right) = \left(- 2\right) \left(x - 1\right)$

This can be converted to other forms:
$\textcolor{w h i t e}{\text{XXX}}$slope-intercept form: $y = m x + b$
$\textcolor{w h i t e}{\text{XXXXXX}} \left(y - 5\right) = \left(- 2\right) \left(x - 1\right)$
$\textcolor{w h i t e}{\text{XXXXXX}}$becomes $y = - 2 x + 7$
or
$\textcolor{w h i t e}{\text{XXX}}$standard form: $A x + B y = C$
$\textcolor{w h i t e}{\text{XXXXXX}} 2 x + y = 7$

Oct 3, 2015

$y = - 2 x + 7$

Explanation:

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

Your slope is $m$, so just subsitute $- 2$ into the equation, which gets you

$y - {y}_{1} = - 2 \left(x - {x}_{1}\right)$

Get your two points that you already have and substitute them into the equation, then expand the brackets to get your final answer.

$y - 5 = - 2 \left(x - 1\right)$
$\Rightarrow$$y - 5 = - 2 x + 2$
$\Rightarrow$ $y = - 2 x + 7$