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A line passes through (-2,-3) and is perpendicular to the line -9x+15y=4. Find it’s x-intercept and y-intercept.

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Answer:

x-intercept and y-intercept of the given line is
\left(-(1)/(5)\right) and
\left((1)/(3)\right)

Solution:

The equation of the line is
-9x+15y=4

Simplifying this we get,


\Rightarrow 9x+15y=4


\Rightarrow 15y =9x+4


\Rightarrow y=\left((9 x)/(15)\right)+\left((4)/(15)\right)

The slope of the line is (9/15), so the slope of the line perpendicular to this will be
(15)/(9)

Let us assume that the y intercept is b, so the equation is
y = mx + b

Now, as that line passes through (-2,-3), hence using this point we get,


-3=\left((15)/(9)\right) *(-2)+b


-3=\left((5)/(3)\right) *(-2)+b


-3=-(10)/(3)+b


-9=-10+3 b


3 b=1


b=\left((1)/(3)\right)

So the equation will be,


y=\left((15)/(9)\right) * x+\left((1)/(3)\right)

Now to find x intercept y =0, Hence,


0=(15 x)/(9)+(1)/(3)


0=(15 x+3)/(9)


(15 x+3)=0


x=-(3)/(15)=-(1)/(5)

To find y intercept x = 0, Hence,


y={((15)/(9)})*0+{((1)/(3)})


\Rightarrow y=(1)/(3)

So, x intercept is
\left(-(1)/(5)\right) and y intercept is
\left((1)/(3)\right)

User Mark Tolonen
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