Respuesta :
Answer:
The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is
[tex]6x+y=-5[/tex]
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( -2 , 7)
To Find:
Equation of Line that passes through the point (-2,7) and is perpendicular to the line x-6y=42=?
Solution:
[tex]x-6y=42[/tex] ..................Given
which can be written as
[tex]y=mx+c[/tex]
Where m is the slope of the line
∴ [tex]y=\dfrac{x}{6}-7[/tex]
On Comparing we get
[tex]Slope = m = \dfrac{1}{6}[/tex]
The Required line is Perpendicular to the above line.
So,
Product of slopes = - 1
[tex]m\times m_{1}=-1\\Substituting\ m\\ \dfrac{1}{6} m_{1}=-1\\\\m_{1}=-6[/tex]
Slope of the required line is -6
Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,
i.e equation in point - slope form
[tex](y-y_{1})=m(x-x_{1})[/tex]
Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2, 7) and slope = -6 we get
[tex](y-7)=-6(x--2)=-6(x+2)=-6x-12\\\\\therefore 6x+y=-5.......is\ the required\ equation\ of\ the\ line[/tex]
The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is
[tex]6x+y=-5[/tex]
