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

Write Equation of a line that goes through (8,5) and is perpendicular to 2x-y=7 in slope intercept form and standard form
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tiepidolu
Converting 2x−y=7 into a slope-intercept form:
y=2x+7

The slope of 2x−y=7 is 2

So the slope of the requiblack 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
$x+2y=18$