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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 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 class=

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jessmzhou4

Answer:  [tex]y=\frac{1}{4}x-7[/tex]

Step-by-step explanation:

The perpendicular slope of the line(m) = [tex]-\frac{1}{m}[/tex]:

  • m = -4 ⇒ [tex]-\frac{1}{m} =-\frac{1}{(-4)} =\frac{1}{4}[/tex]

The function formula is y = mx + b, where the y-intercept(b) is found by substituting in the values of a point on the line ⇒ (4, -6):

[tex]y=\frac{1}{4}x+b\\-6=\frac{1}{4}(4)+b\\-6=1+b\\b=-6-1=-7[/tex]

So the perpendicular equation is [tex]y=\frac{1}{4}x-7[/tex].

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