SOLUTION: Write an equation of the line contaning the given point and perpendicular to the givin line
(3,-6); 4x+9y=7
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Question 521342: Write an equation of the line contaning the given point and perpendicular to the givin line
(3,-6); 4x+9y=7
Found 2 solutions by mananth, Maths68:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
4 x + 9 y = 7
Find the slope of this line
9 y = -4 x + 7
Divide by 9
y = 0 x + 0.78
Compare this equation with y=mx+b
slope m = -0.44
The slope of a line perpendicular to the above line will be the negative reciprocal 2.25
m1*m2=-1
The slope of the required line will be 2.25
m= 2 1/4 ,point ( 3 , -6 )
Find b by plugging the values of m & the point in
y=mx+b
-6 = 6.75 + b
b= -12.75
m= 9/4
The required equation isy = 9/ 4 x-51/ 4
m.ananth@hotmail.ca
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Given
Point (x, y)=(3,-6)
Line: 4x+9y=7
Rearrange the equation according to equation of standard form
4x+9y=7
9y=-4x+7
9y/9=(-4x+7)/9
y=(-4/9)x+7/9
Compare above equation with the equation of line slope-intercept form
y=mx+b
m=-4/9 and b=7/9
Slope of the given line m =-4/9 and y-intercept = b =7/9
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 (9/4)
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Now we have a point (3,-6) and slope (9/4) 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
-6=(9/4)(3)+b
-6=27/4+b
-6-27/4=b
-24-27/4=b
-51/4=b
b=-51/4
y-intercept of the required line =b=-51/4
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Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form
y=mx+b
y=(9/4)x-51/4
Above equation is the required equation of the line
Red Line = y =(-4/9)x+7/9
Green Line = y =(9/4)x-51/4
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