# How do you write Equation of a line that goes through (8,5) and is perpendicular to 2x-y=7 in slope intercept form and standard form?

May 5, 2015

Converting $2 x - y = 7$ into a slope-intercept form:
$y = 2 x + 7$

The slope of $2 x - y = 7$ is $2$

So the slope of the required line is $- \frac{1}{2}$
(the slopes of perpendicular lines are the negative inverse of each other)

We are looking for a line with slope $m = - \frac{1}{2}$ which passes through
$\left({x}_{1} , {y}_{1}\right) = \left(8 , 5\right)$

In slope-point form this is
$\left(y - 5\right) = \left(- \frac{1}{2}\right) \left(x - 8\right)$

Converting to slope intercept form:
$y = - \frac{1}{2} x + 9$

and in standard form
$x + 2 y = 18$