Question

A walking path across a park is represented by the equation y=-4x+10. A new path will be built perpendicular to this path. The paths will intersect at the point (4,-6). Identify the equation that represents the new path. A. y=4x-22 B. y=1/4x-7 C. y=-4x+10 D. y=-1/4x-5

Answer 1

Given:

The equation of a line is

`y=-4x+10`

A perpendicular line on the given line passes through the point (4,-6).

To find:

The equation of the perpendicular line.

Solution:

We have,

`y=-4x+10`

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

`m=-4`

So, the slope of the given line is -4.

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

`m* m_1=-1`

`(-4)* m_1=-1`

`m_1=(-1)/(-4)`

`m_1=(1)/(4)`

The slope of the required line is
`(1)/(4)` and it passes through the point (4,-6). So, the equation of the line is

`y-y_1=m_1(x-x_1)`

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

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

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

`y=(1)/(4)x-7`

Therefore, the correct option is B.