Question

A walking path across a park is represented by the equation y= -3x - 6 . A new path will be built perpendicular to this path. The path will intersect at the point (-3 , 3) . Identify the equation that represents the new path . WILL MARK BRAINIEST!

Answer 1

Answer:

C.  $y=\frac{1}{3}x+4$

Step-by-step explanation:

We are given the path, $y=-3x-6$.

The general form of the straight line is 'y=mx+b', where 'm' is the slope and 'b' is the y-intercept.

Thus, the slope of the given line is -3.

As, we have that the new path is perpendicular to the given path.

And, we know that, 'Product of slopes of perpendicular lines is -1'.

So, we get,

$m\times (-3)=-1$

i.e. $m=\frac{1}{3}$.

Since, the new path passes through the point (-3,3). Substituting the values in the general form, we get,

$3=\frac{1}{3}\times (-3)+b$

i.e. $3=-1+b$

i.e. b= 3+1

i.e. b= 4.

Hence, the equation representing the new path is $y=\frac{1}{3}x+4$.

Thus, option C is correct.