SOLUTION: Find the equation of the line perpendicular to 4x-5y=3 through (2,3).

Question 631910: Find the equation of the line perpendicular to 4x-5y=3 through (2,3).

Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Given
Point (x, y)=(2,3)
Line:
4x-5y=3
-5y=-4x+3
-5y/-5=(-4x+3)/-5
y=-4x/-5-3/5
y=(4/5)x-3/5
Compare above equation with the equation of line slope-intercept form
y=mx+b
m=4/5 and b=-3/5
Slope of the given line m = 4/5 and y-intercept = b = -3/5
Since required line is perpendicular, the multiplication of the slopes of both lines result in (-1), therefore the slope of the required line will be (-5/4)
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Now we have a point (2,3) and slope (-5/4) of the required line we can easily find the required line put these values in the equation of slope-intercept form to find the y-intercept of the required line
y=mx+b
3=(-5/4)(2)+b
3=-10/4+b
3+10/4=b
(12+10)/4=b
22/4=b
11/2=b
b=11/2
y-intercept of the required line = b = 11/2 and slope = m = -5/4
Put the values of �m� and �b� in equation of the line slope-intercept form
y=mx+b
y=(-5/4)x+11/2
Above equation is the required equation of the line in slope-intercept form.

Graph
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y=(4/5)x-3/5 (Given line)
y=(-5/4)x+11/2(Required line)

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