Respuesta :
Given:
Street C is perpendicular to Street A and passes through (4, -6).
The equation of street A is:
[tex]y=-2x+2[/tex]
To find:
The equation of street C.
Solution:
The equation of street A is:
[tex]y=-2x+2[/tex]
On comparing this equation with slope intercept form [tex]y=mx+b[/tex], we get
[tex]m_2=-2[/tex]
Slope of this line is -2.
We know that, the product of slopes of two perpendicular lines is always -1.
[tex]m_1\times m_2=-1[/tex]
[tex]m_1\times (-2)=-1[/tex]
[tex]m_1=\dfrac{-1}{-2}[/tex]
[tex]m_1=\dfrac{1}{2}[/tex]
The slope of street C is [tex]m_1=\dfrac{1}{2}[/tex] and it passes through the point (4,-6). So, the equation of street C is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-6)=\dfrac{1}{2}(x-4)[/tex]
[tex]y+6=\dfrac{1}{2}(x-4)[/tex]
Therefore, the point slope form of the street C's equation is [tex]y+6=\dfrac{1}{2}(x-4)[/tex].
