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Through: (-5, -3), perp. to y=-9/4x-5

1 Answer

4 votes

Given:

A line passes through (-5,-3) and perpendicular to
y=-(9)/(4)x-5.

To find:

The equation of the line.

Solution:

We have,


y=-(9)/(4)x-5

On comparing this equation with slope intercept form, i.e.,
y=mx+b, we get


m_2=-(9)/(4)

It means, slope of this line is
-(9)/(4).

Product of slopes of two perpendicular lines is always -1.


m_1* m_2=-1


m_1 * \left(-(9)/(4)\right)=-1


m_1=(4)/(9)

Slope of required line is
(4)/(9) and it passes through the point (-5,-3). So, the equation of the line is


y-y_1=m(x-x_1)

where, m is slope.


y-(-3)=(4)/(9)(x-(-5))


y+3=(4)/(9)(x+5)


9(y+3)=4(x+5)


9y+27=4x+20


27-20=4x-9y


7=4x-9y

Therefore, the equation of required line is
4x-9y=7.

User Climatebrad
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