Given:
The equations of lines are
[tex]y=\dfrac{4}{5}x+8[/tex]
[tex]20y+25x=180[/tex]
To find:
The relation between two of lines.
Solution:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
We have,
[tex]y=\dfrac{4}{5}x+8[/tex] ...(i)
[tex]20y+25x=180[/tex] ...(ii)
Equation (i) can be written as
[tex]20y=-25x+180[/tex]
[tex]y=\dfrac{-25x+180}{20}[/tex]
[tex]y=\dfrac{-25x}{20}+\dfrac{180}{20}[/tex]
[tex]y=\dfrac{-5x}{4}+9[/tex] ...(iii)
On comparing (i) with slope intercept form, we get
[tex]m_1=\dfrac{4}{5}[/tex]
On comparing (iii) with slope intercept form, we get
[tex]m_2=-\dfrac{5}{4}[/tex]
Now,
[tex]m_1\times m_2=\dfrac{4}{5}\times (-\dfrac{5}{4})[/tex]
[tex]m_1\times m_2=-1[/tex]
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.
