What is the equation of the line which is perpendicular to $2 x + y = - 4$ $2x+y=-4$ which passes through the point $(2, - 8) ?$ $(2,-8)?$

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Answer 1 · 2017-11-17T19:48:36

$y = \frac{1}{2} x - 9$ $y = 1/2x - 9$

Given equation : $2 x + y = - 4$ $2x + y = - 4$

We rewrite this in Slope-Intercept form, that is;

$y = - 2 x - 4$ $y = -2x - 4$

The slope in this equation's case is $m = - 2$ $m = -2$

Therefore, the slope of a line that is perpendicular to this line is going to be the negative reciprocal of the given slope.

$m = - (- \frac{1}{2}) = \frac{1}{2}$ $m = -(-1/2) = 1/2$

The y-intercept can be determined from the coordinates provided.
$(2, - 8) .$ $(2,-8).$

Substitute the values of the x and y coordinate in its Slope-Intercept form to determine the $y$ $y$ -intercept:

$y = m x + b$ $y = mx + b$
$- 8 = (\frac{1}{2}) (2) + b$ $-8 = (1/2)(2) + b$
$b = - 9$ $b = -9$

Therefore, the equation of the line is $y = \frac{1}{2} x - 9$ $y = 1/2x - 9$

What is the equation of the line which is perpendicular to 2x+y=−42x+y=-4 which passes through the point (2,−8)?(2,-8)?