SOLUTION: Equation of the line containing the given point and perpendicular to the given line (7,-6);6x+5y=4

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Question 1184279: Equation of the line containing the given point and perpendicular to the given line (7,-6);6x+5y=4
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
(7,-6)
6x%2B5y=4
perpendicular lines have slopes negative reciprocal to each other
so, first find a slope of the given line
6x%2B5y=4........solve for y
5y=-6x%2B4
y=-%286%2F5%29x%2B4%2F5
=> slope m=-%286%2F5%29
negative reciprocal is m=-1%2F%28-%286%2F5%29%29=5%2F6 -> a slope of the perpendicular line
use point-slope formula to find equation
y-y%5B1%5D=m%28x-x%5B1%5D%29.........plug in m=5%2F6 and coordinates of the point (7,-6)
y-%28-6%29=%285%2F6%29%28x-7%29
y%2B6=%285%2F6%29x-7%285%2F6%29
y=%285%2F6%29x-7%285%2F6%29-6
y=%285%2F6%29x-71%2F6




Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Equation of the line containing the given point and perpendicular to the given line (7,-6);6x+5y=4
As the given equation is in standard form, we switch the variables' coefficients, negate the new

y-coordinate, and then substitute the given coordinates on the right side to get the constant.

In other words, 6x + 5y = 4 becomes: 5x - 6y = 5(7) - 6(- 6)

5x - 6y = 35 + 36

5x - 6y = 71 <==== Equation of the line sought.