Question

A walking path across a park is represented by the equation y=-3x - 3. A

new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 6). Identify the equation that represents the new path.
OA. y=-3x-6
O B. y=x+7
OC. y=3x+15
O D. y=-x+5
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Answer 1

Y=1/3x + 7 is the correct answer

Answer 2

y = (1/3)x + 7

Explanation:

The general structure form of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.

The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.

m = 1/3

x = -3

y = 6

y = mx + b <----- Slope-intercept form

6 = (-3)(1/3) + b <----- Insert values

6 = -1 + b <----- Multiply -3 and 1/3

7 = b <----- Add 1 to both sides

Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.

y = (1/3)x + 7