# How do you write the equation in point slope form given point (6,1) and perpendicular to y=-x+6?

May 13, 2018

$y - 1 = x - 6$

#### Explanation:

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

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$y = - x + 6 \text{ is in this form}$

$\text{with slope m } = - 1$

$\text{given a line with slope m then the slope of a line}$
$\text{perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{- 1} = 1$

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

•color(white)(x)y-y_1=m(x-x_1)

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

$\text{here "m=1" and } \left({x}_{1} , {y}_{1}\right) = \left(6 , 1\right)$

$\Rightarrow y - 1 = 1 \left(x - 6\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$