SOLUTION: write the equation of the line that passes through the point (2, -4) and is perpendicular to the to the line described by x+2y=12

Question 1148569: write the equation of the line that passes through the point (2, -4) and is perpendicular to the to the line described by x+2y=12
Found 2 solutions by rothauserc, greenestamps:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
x +2y = 12
:
rewrite the line's equation in slope y-intercept form
:
y = -x/2 +6
:
slope of the line is -1/2
:
the slope of the line perpendicular to our line is the negative reciprocol
:
slope is -(1/(-1/2)) = 2
:
using the slope y-intercept form
:
y = 2x +b
:
now subsitute the x coordinate for x and the y coordinate for y using the given point
:
-4 = 2(2) +b
:
b = -8
:
y = 2x -8
:
the general form is
:
2x -y = 8
:

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Every line parallel to x+2y=12 will have an equation of the form x+2y=C for some constant C; every line perpendicular to x+2y=12 will have an equation of the form 2x-y=C for some constant C. (Switch the two coefficients and make one of them negative; "1 and 2" becomes "2 and -1".)

So the equation is of the form 2x-y=C, and the point (2,-4) is on the line. So

So an equation of the line you are looking for is 2x-y = 8.

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