How do you graph the line through (2,-9) perpendicular to x + 2y = 8?

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Answer 1 · 2017-06-27T13:34:13

See below.

We must first find the slope of the given line.

$x + 2 y = 8$ $x+2y=8$

$2 y = 8 - x$ $2y=8-x$

$y = 4 - \frac{1}{2} x$ $y=4-1/2x$

So, the perpendicular line's slope is the opposite inverse of the given line, or $2$ $2$ .

Since we are given that it passes through a point, we may use point-slope to write out the line.

Point-Slope: $y - y_{0} = m (x - x_{0})$ $y-y_0=m(x-x_0)$

Plugging in,

$y - (- 9) = 2 (x - 2)$ $y-(-9)=2(x-2)$

$y = 2 x - 4 - 9$ $y=2x-4-9$

$y = 2 x - 13$ $y=2x-13$

We can now graph this.

graph{2x-13 [-12.58, 27.42, -8.44, 11.56]}