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.

Answer 1

Answer:  $y=\frac{1}{4}x-7$

Step-by-step explanation:

The perpendicular slope of the line(m) = $-\frac{1}{m}$:

• m = -4 ⇒ $-\frac{1}{m} =-\frac{1}{(-4)} =\frac{1}{4}$

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):

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

So the perpendicular equation is $y=\frac{1}{4}x-7$.