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 $\frac{2}{1}$, we are going to flip it to make it $\frac{1}{2}$ and change the sign to make it $-\frac{1}{2}$.

So now we know that the slope of the perpendicular line is $-\frac{1}{2}$, we can start a new equation for this line:

$y=-\frac{1}{2}x+b$

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:

$-3=-\frac{1}{2}(-2)+b$

Then solve for b:

$-3=1+b$

$b=-4$

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

$y=-\frac{1}{2}x-4$

So this equation now represents the new path.