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Free_Kalibri [48]
3 years ago
12

Help with this one because I do not know how to do perpendicular plz put explanation with steps worth 50!

Mathematics
1 answer:
Yuri [45]3 years ago
3 0

Answer:

Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line 2x-3y=12 is 3x+2y=34  

Step-by-step explanation:

Given:  

2x-3y=12  

To Find:  

Equation of line passing through ( 16, -7) and is perpendicular to the line  

2x-3y=12  

Solution:  

2x-3y=12 ...........Given  

\therefore y=\dfrac{2}{3}\times x-4

Comparing with,  

y=mx+c  

Where m =slope  

We get  

Slope = m1 = \dfrac{2}{3}  

We know that for Perpendicular lines have product slopes = -1.

m1\times m2=-1

Substituting m1 we get m2 as

\dfrac{2}{3}\times m2=-1\\\\m2=-\dfrac{3}{2}

Therefore the slope of the required line passing through (16 , -7) will have the slope,

m2=-\dfrac{3}{2}  

Now the equation of line in slope point form given by  

(y-y_{1})=m(x-x_{1})  

Substituting the point (16 , -7) and slope m2 we will get the required equation of the line,  

(y-(-7))=-\dfrac{3}{2}\times (x-16)\\\\2y+14=-3x+48\\3x+2y=34......Equation\ of\ line  

Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line  2x-3y=12 is

3x+2y=34  

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