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PolarNik [594]
2 years ago
10

What is the equation of the line perpendicular to the line y=4/9x-2 that passes through the line 4,3

Mathematics
2 answers:
alukav5142 [94]2 years ago
6 0

Given

The line equation is        

y= \frac{4}{9}x-2

passes through the line (4,3 )

Find out the equation of the perpendicular line.

To proof

given equation is

 y= \frac{4}{9}x-2

the equation of line is in the form y = mx +c

where m = slope

           c is the intercept on the y axis.

compare this equation to the above equation

we get

m =\frac{4}{9}

In perpendicular line case

The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.

thus slope of the perpendicular line

= \frac{-9}{4}

Than equation perpendicular line becomes

y= \frac{-9}{4}x + c

as the line passes through the point( 4,3)

put these value in the above equation

we get

3= \frac{-9}{4}\times 4 + c

solving the above equation

3 +9 =c

12 =c

put this value in the above equation

we get

y= \frac{-9}{4}\times x + 12

this is equation of the perpendicular line.

Hence proved



skad [1K]2 years ago
6 0
Y=-9/4x-3 (the slope to a perpendicular pair is the reciprocal of the opposite)
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