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

Given:

The equation of a line is

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

To find:

The equation of the perpendicular line.

Solution:

We have,

On comparing this equation with slope intercept form , we get

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

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

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

Therefore, the correct option is B.

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step-by-step explanation: