SOLUTION: line perpendicular to x-2y=24 and passing through (1,-3)

Question 153575: line perpendicular to x-2y=24 and passing through (1,-3)
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
line perpendicular to x-2y=24 and passing through (1,-3)
.
First, rearrange your expression to the "slope intercept" form:
y = mx + b
where
m is slope
b is the y-intercept
.
Your equation:
x-2y=24
-2y = -x + 24
y = (1/2)x - 12
.
Now, we know that the "slope" (m) of
x-2y=24
is 1/2
.
A line perpendicular to the above MUST be the negative reciprocal:
If our new slope is M then:
(1/2)M = -1
M = -2
Therefore, our NEW line has a slope (m) of -2
.
Recapping:
We now know our new line has
slope (m) = -2
AND
it passes through:
(1,-3)
.
Plug the above back into the "slope intercept" form and solve for 'b':
y = mx + b
-3 = (-2)(1) + b
-3 = -2 + b
-1 = b
.
We NOW know:
b = -1
m = (1/2)
.
Plugging it into:
y = mx + b
y = (1/2)x + (-1)
or
y = (1/2)x - 1 (this is your answer!)

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