SOLUTION: Find an equation of the line satisfying the given conditions. Through (7,2); Perpendicular to 4x+9y=46

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Question 266980: Find an equation of the line satisfying the given conditions.
Through (7,2); Perpendicular to 4x+9y=46

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Find an equation of the line satisfying the given conditions.
Through (7,2); Perpendicular to 4x + 9y = 46
:
Put the equation in the slope intercept form to find the slope (y = mx + b)
4x + 9y = 46
9y = -4x + 46
Divide by 9
y = -4%2F9x + 46%2F9
Slope (m1) = -4%2F9
:
Slope relationship of perpendicular lines: m1*m2 = -1
find m2
-4%2F9*m2 = -1
m2 = -1 * -9%2F4
m2 = 9%2F4 is the slope of the perpendicular line
:
Use the point/slope equation y - y1 = m(x - x1); x1=7, y1=2
y - 2 = 9%2F4(x - 7)
:
y - 2 = 9%2F4x - 9%2F4(7)
:
y - 2 = 9%2F4x - 63%2F4
:
y = 9%2F4x - 63%2F4 + 2
:
y = 9%2F4x - 63%2F4 + 8%2F4
:
y = 9%2F4x - 55%2F4, the equation of the perpendicular line