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Question 488082: what is the equation of a line through (4, 10) which is perpendicular to the line y=3x+2
Answer by Jstrasner(112)   (Show Source):
You can put this solution on YOUR website! Hey,
So for this one we need to see what we have and fit it all together. First of all, if the line that we are looking for is perpendicular to the line given, then the slope of the line must be the negative reciprocal of the slope of the line given:
3x => -(1/3)x
Now to find the coordinates of the second line, we need to plug in the points that it goes through into the equation: y= mx + b (m being the slope which in this case is -(1/3), and b being the point where the line crosses the y-axis). So now we need to put the coordinates in:
y = -(1/3)x + b => 10 = -(1/3)(4) + b => 10 = -(4/3) + b. Now we need to solve for b, so we want to isolate it by getting rid of the -(4/3):
-(3/4) (10) = -(3/4)(-(4/3) + b => -(15/2) = b. So now that we have b and the slope of the second line we have the formula for the second line:
y = -(1/3)x -(15/2)
I hope this helps!
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