Answer:
The slopes are
[tex]m1=\dfrac{2}{5}, m2=-\dfrac{5}{2}[/tex]
Therefore, the equations are equations of Perpendicular Lines .
Step-by-step explanation:
Given:
[tex]y=\dfrac{2}{5}\times x + 1[/tex] ......................Equation ( 1 )
[tex]5x+2y=-4\\\\\therefore y = \dfrac{-5}{2}\times x-2[/tex] ..............Equation ( 2 )
To Find:
Slope of equation 1 = ?
Slope of equation 2 = ?
Solution:
On comparing with slope point form
[tex]y=mx+c[/tex]
Where,
m = Slope
c = y-intercept
We get
Step 1.
Slope of equation 1 = m1 = [tex]\dfrac{2}{5}[/tex]
Step 2.
Slope of equation 1 = m2 = [tex]-\dfrac{5}{2}[/tex]
Step 3.
Product of Slopes = m1 × m2 = [tex]\dfrac{2}{5}\times -\dfrac{5}{2}=-1[/tex]
Product of Slopes = m1 × m2 = -1
Which is the condition for Perpendicular Lines
The slopes are
[tex]m1=\dfrac{2}{5},m2=-\dfrac{5}{2}[/tex]
Therefore, the equations are equations of Perpendicular Lines .
