Question 491516: write the equation of a line that is perpendicular to the given line and that passes through the given point. 4x-12y=2;(10,-1)
Answer by Jstrasner(112)   (Show Source):
You can put this solution on YOUR website! Hey,
So for this problem we need to look at what we have and construct another equation. First we should put the equation into terms that are most common, with y on one side and everything else on the other:
4x - 12y = 2 => -12y = 2 - 4x => 12y = -2 + 4x => y = -(2/12) + (4/12)x => y = (1/3)x - (1/6)
We can disregard the last number as it is specific to this line and not the one we are looking for.
Second, we need to figure out the slope of the first line to find the slope of the second line. The slope of the first line is (1/3). The lines are perpendicular, which means that their slopes are both reciprocal and negative of each other: first line: (1/3) second line: -3
The equation of a line is y = mx + b, where m is the slope which we have, and b is the coordinate on the y axis that the line crosses. We know the slope (-3). To find the b coordinate, we need to plug in the coordinates we were given at the beginning of the problem (10, -1):
y = -3x + b => -1 = -3(10) + b => -1 = -30 + b => 29 = b. Now we have the b coordinate and can construct a final formula:
y = -3x + 29
I know its confusing but just reread this and you will understand it.
I hope this helps!
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