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 paths will intersect at the point (-3,3). Identify the equation that represents the new path 10- 20 10​

Answer 1

B

Explanation:

> if the lines are perpendicular then their slopes are negative reciprocal so

y=mx+b , is the general form where is m = slope

y= -3x -4, old path has slope m= -3

y= (1/3)x +b , is the new path with slope m=(1/3)

>if the paths intersect at (-3,3) then this point is on the new path as well

y= (1/3)x +b, now substitute x= -3, and y=3 to find b

3 = (1/3)(-3)+b , divide -3/3

3= -1 +b, add 1 to both sides

4 = b

>the equation of the new path is

y= (1/3)x +4

Answer 2

The equation of the new path would be y=1/3x+4.

Explanation

If two lines are perpendicular, their slopes are negative reciprocals of each other. The original equation is written in slope-intercept form, y=mx+b, where m is the slope. In this equation, m=-3=-3/1.

In the new equation, the slope would be the opposite sign and flipped; this means it would be 1/3.

We can use the point given, the slope and slope-intercept form to write the equation of the new line:

y=mx+b

3=1/3(-3)+b

3=1/3(-3/1)+b

3=(-3/3)+b

3=-1+b

Add 1 to both sides:

3+1=-1+b+1

4=b

This makes the equation y=1/3x+4.