What is the equation of a line perpendicular to the line $y - 2 x = 5$ $y-2x=5$ and goes through (1,2)?

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Answer 1 · 2015-11-14T03:31:52

$y = \frac{- x + 5}{2}$ $y=\frac{-x+5}{2}$

$y = 2 x + 5$ $y=2x+5$

We can see that the slope $m = 2$ $m=2$ . If you want a line perpendicular to your function, then the slope would be $m'=-1/m=-1/2$ .

And so, you want your line to go through $(1,2)$ . Using the point-slope form:

$y-y_0=m'(x-x_0)$

$y-2=-0.5(x-1)$

$y-2=-0.5x+0.5$

$y=-0.5x+0.5+2$

$y=-0.5x+2.5$

$y=-1/2x+5/2$

$y=\frac{-x+5}{2}$

The red line is the original function, the blue one is the perpendicular which goes through $(1,2)$ .

What is the equation of a line perpendicular to the line y-2x=5y−2x=5y-2x=5 and goes through (1,2)?