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WITCHER [35]
3 years ago
15

What is the equation of the line that passes through (6, 1) and is perpendicular to the line y 3x+2? CI) At what angle do the li

nes y= 6x +4 and y-2x+3 cross?
Mathematics
1 answer:
Andrews [41]3 years ago
8 0

Answer with explanation:

The equation of any line with slope 'm' and passing through any point (x_1,y_1) is given by

y=mx+(y_1-mx_1)

As we know that the general equation of a line with slope 'm' is y=mx+c

Comparing with the given equation y=3x+2 we can conclude slope of the given line is m_1=3

Now we know that the product of slopes of perpendicular lines is -1

Mathematically we can write for perpendicular lines

m_1\times m_2=-1

Thus the slope of the required line is obtained from the above relation since it is given that they are perpendicular

3\times m_{2}=-1\\\\\therefore m_{2}=\frac{-1}{3}

Hence using the given and the obtained values the equation of the required line is

y=-\frac{1}{3}x+(1-\frac{-1}{3}\times 6)}\\\\y=\frac{-x}{3}+3

Part b)

The angle of intersection between 2 lines with slopes m_{1},m_2 is given by

\theta =tan^{-1}(\frac{m_2-m_1}{1+m_1m_2})

Comparing the equations of given lines

y=6x+3\\\\y=2x+3

with the standard equation we get

m_{1}=6\\\\m_{2}=2

Thus the angle of intersection becomes

\theta =tan^{-1}(\frac{2-6}{1+2\times6})=17.10

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Hope I helped! :)
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