Walking path across the park is represented by the equation y=-2x-7.a new path will be built perpendicular to this path. the past will intersect at the point (-2,-3) identify the equation that represents the new path

here the equation of path is -2x-7=y

let us find slope of this line by using y=mx+b

so slope m=-2

now new path is perpendicular to this path.

product of slopes of perpendiculars is -1

so slope of new path is 1/2

now it passes through (-2,-3) with slope 1/2

using y=mx+b to get value of b

-3=1/2(-2) +b

b=-2

plugging m=-1/2 and b=-2 in y=mx + b to get the final equation as

y=(-1/2) x -2 is the equation of new path

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)