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The lines represented by the equations y=\frac{4}{5}x+8y= 5 4 ​ x+8 and 20y+25x=18020y+25x=180 are

User Sdouble
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1 Answer

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Given:

The equations of lines are


y=(4)/(5)x+8


20y+25x=180

To find:

The relation between two of lines.

Solution:

The slope intercept form of a line is


y=mx+b

Where, m is slope and b is y-intercept.

We have,


y=(4)/(5)x+8 ...(i)


20y+25x=180 ...(ii)

Equation (i) can be written as


20y=-25x+180


y=(-25x+180)/(20)


y=(-25x)/(20)+(180)/(20)


y=(-5x)/(4)+9 ...(iii)

On comparing (i) with slope intercept form, we get


m_1=(4)/(5)

On comparing (iii) with slope intercept form, we get


m_2=-(5)/(4)

Now,


m_1* m_2=(4)/(5)* (-(5)/(4))


m_1* m_2=-1

The product of slopes of both lines is -1. We know that the product of slopes of two perpendicular lines is -1.

Therefore, the given lines are perpendicular.

User Naudster
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