Question

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

Answer 1

Given:

The equations of lines are

$y=\dfrac{4}{5}x+8$

$20y+25x=180$

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,

$y=\dfrac{4}{5}x+8$        ...(i)

$20y+25x=180$          ...(ii)

Equation (i) can be written as

$20y=-25x+180$

$y=\dfrac{-25x+180}{20}$

$y=\dfrac{-25x}{20}+\dfrac{180}{20}$

$y=\dfrac{-5x}{4}+9$             ...(iii)

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

$m_1=\dfrac{4}{5}$

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

$m_2=-\dfrac{5}{4}$

Now,

$m_1\times m_2=\dfrac{4}{5}\times (-\dfrac{5}{4})$

$m_1\times m_2=-1$

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.