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Give the equation of a line that goes through the point ( − 21 , 2 ) and is perpendicular to the line 7 x − 4 y = − 12 . Give your answer in slope intercept form

User Gweg
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1 Answer

3 votes

Given:

Equation of line
7x-4y=-12.

To find:

The equation of line that goes through the point ( − 21 , 2 ) and is perpendicular to the given line.

Solution:

The given equation of line can be written as


7x-4y+12=0

Slope of line is


\text{Slope}=-\frac{\text{Coefficient of x}}{\text{Coefficient of y}}


m_1=-(7)/((-4))


m_1=(7)/(4)

Product of slopes of two perpendicular lines is -1. So, slope of perpendicular line is


m_1m_2=-1


m_2=-(1)/(m_1)


m_2=-(4)/(7)
[\because m_1=(7)/(4)]

Now, the slope of perpendicular line is
m_2=(4)/(7) and it goes through (-21,2). So, the equation of line is


y-y_1=m_2(x-x_1)


y-2=-(4)/(7)(x-(-21))


y-2=-(4)/(7)x-(4)/(7)(21)


y-2=-(4)/(7)x-12


y=-(4)/(7)x-12+2


y=-(4)/(7)x-10

Therefore, the required equation in slope intercept form is
y=-(4)/(7)x-10.

User Kludg
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