Question

Street C is perpendicular to Street A and passes through

(4, -6). Write this street's equation in point- slope form.
street a's equation was y= -2x +2

Answer 1

Given:

Street C is perpendicular to Street A and passes through (4, -6).

The equation of street A is:

`y=-2x+2`

To find:

The equation of street C.

Solution:

The equation of street A is:

`y=-2x+2`

On comparing this equation with slope intercept form
`y=mx+b`, we get

`m_2=-2`

Slope of this line is -2.

We know that, the product of slopes of two perpendicular lines is always -1.

`m_1* m_2=-1`

`m_1* (-2)=-1`

`m_1=(-1)/(-2)`

`m_1=(1)/(2)`

The slope of street C is
`m_1=(1)/(2)` and it passes through the point (4,-6). So, the equation of street C is

`y-y_1=m(x-x_1)`

`y-(-6)=(1)/(2)(x-4)`

`y+6=(1)/(2)(x-4)`

Therefore, the point slope form of the street C's equation is
`y+6=(1)/(2)(x-4)`.