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 represents the new path

Answer 1

The equation that represents the new path is: $y = \frac{1}{4}x-7$

Step-by-step explanation:

Given path is:

$y=-4x+10$

We have to find the equation of a path that will be perpendicular to given path and will pass through point (4,-6)

So first of all we have to find the slope of given line

As the equation of path is in slope-intercept form, the coefficient of x will be the slope of the path

so

m = -4

As the product of slopes of two perpendicular lines is -1

Let m1 be the slope of required line

$m.m_1 = -1\\-4 . m_1 = -1\\m_1 = \frac{-1}{-4}\\m_1 = \frac{1}{4}$

The slope-intercept form is:

$y=m_1x+b$

Putting the value of m1

$y = \frac{1}{4}x+b$

Putting the point (4,-6) in the equation

$-6 = \frac{1}{4}(4) +b\\-6 = 1+b\\b = -6-1\\b = -7$

Putting the value of b

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

So,

The equation that represents the new path is: $y = \frac{1}{4}x-7$

Keywords: Equation of line, slope

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