Question 1111377: Find the equation of the line which passes through the point (-3,5) and is perpendicular to the line 4x+3y=6. Express your answer in slope-intercept form.
Found 4 solutions by Alan3354, stanbon, ikleyn, amalm06:
Answer by Alan3354(69443)   (Show Source):
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Find the equation of the line which passes through the point (-3,5) and is perpendicular to the line 4x+3y=6. Express your answer in slope-intercept form.
Find the slope of the given equation.
y = (-4/3)x + 2
slope = -4/3
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Find the slope of a line that is perpendicualar to the given line.
m = (3/4)
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Ans Form:: y = mx + b
Solve for "b" if m = 3/4, x = -3, y = 5.
5 = (3/4)(-3) + b
5 = -9/4 + b
29/4 = b
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Ans:: y = (3/4)x + (29/4)
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Cheers,
Stan H.
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Answer by ikleyn(52879)  (Show Source):
Answer by amalm06(224)  (Show Source):
You can put this solution on YOUR website! You can use calculus to find the slope.
4x+3y=6
3y=6-4x
y=(-4/3)x+2
Differentiate implicitly:
dy=(-4/3)dx
dy/dx=-4/3
The slope of the line in question must be 3/4, since the product of the slopes of two perpendicular lines is -1.
To find the y-intercept of the line in question, note that the line passes through (-3,5). So that
5=(3/4)(-3)+b
b=29/4
Therefore, the equation of the line in question is
y=(3/4)x+(29/4)
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