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Question 150191: find the equation of the line through (4,3) perpendicular to the line 3x+y=7.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Step 1:
determine slope of:
3x+y=7
Subtracting 3x from both sides we get:
y = -3x +7
This happens to be in the "slope-intercept" form:
y = mx + b
where
m is slope
b is y-intercept
.
Now, we know the slope = -3
.
Step 2:
Determine slope of new line (perpendicular to first)
A line is perpendicular to another if their slopes are negative reciprocal:
Let m=new slope
(-3)m = -1
m = (-1)/(-3) = 1/3
Plug the above along with the given point of (4,3) into the "slope intercept" formula and solve for b:
y = mx + b
3 = (1/3)(4) + b
9 = 4 + 3b
5 = 3b
5/3 = b
Now, that you have 'm' and 'b' stuff it back into:
y = mx + b
To get your final answer:
y = (1/3)x + (5/3)
or
y = .33x + 1.67
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