Question

A walking path across a park is represented by the equation Y equals negative 2X -7. A new path will be built perpendicular to this path. The Pats will intersect at the point -2, -3. Identify the equation that represents the new path

Answer 1

So we are given an initial equation of:
`y=2x-7`.

We are told that a new path is going to be perpendicular to this line. So to find a slope that is perpendicular to a line, we take the slope of the known line (in this case 2) and we flip it and change the sign. So since this slope is essentially
`(2)/(1)`, we are going to flip it to make it
`(1)/(2)` and change the sign to make it
`-(1)/(2)`.

So now we know that the slope of the perpendicular line is
`-(1)/(2)`, we can start a new equation for this line:

`y=-(1)/(2)x+b`

We are also told that the path will intersect at (-2,-3) - this is a solution to the two lines. So to find b in this new equation, let's plug in the x and y values found in the point:

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

Then solve for b:

`-3=1+b`

`b=-4`

So then we plug in our value for b and leave x and y:

`y=-(1)/(2)x-4`

So this equation now represents the new path.