Question

A walking path across a park is represented by the equation y=-2x+5. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-2,9). Identify the equation that represents the new path.
A. y= {x+10
B. y= -2x - 5
C. y= 2x+13
D. y -- 1x+8

Answer 1

Answer:

$y = \frac{1}{2}x+10$

Step-by-step explanation:

The given path is:

y = -2x+5

Comparing with the standard form of equation:

y = mx+b

So,

m = -2

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

Let m1 be the slope of the perpendicular line

m*m1=-1

-2*m1 = -1

m1 = -1/-2

m1 = 1/2

So the slope of perpendicular path is 1/2.

Since the new path passes through (-2,9)

$9 = \frac{1}{2}(-2) +b\\9 = -1 +b\\b = 10$

Putting the values of m and b in standard form

$y = \frac{1}{2}x+10$

Hence the equation of new path is:

$y = \frac{1}{2}x+10$ ..