The equation that represents the new path is: 
Step-by-step explanation:
Given path is:

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

The slope-intercept form is:

Putting the value of m1

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

Putting the value of b

So,
The equation that represents the new path is: 
Keywords: Equation of line, slope
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