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.

$m\times m_1=-1$

$(-4)\times m_1=-1$

$m_1=\dfrac{-1}{-4}$

$m_1=\dfrac{1}{4}$

The slope of the required line is $\dfrac{1}{4}$ and it passes through the point (4,-6). So, the equation of the line is

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

$y-(-6)=\dfrac{1}{4}(x-4)$

$y+6=\dfrac{1}{4}x-1$

$y=\dfrac{1}{4}x-1-6$

$y=\dfrac{1}{4}x-7$

Therefore, the correct option is B.