Question

What equation will describe the location of Negative Reciprocal Road? What equation will describe the location of Slope Street?

Answer 1

(a)

If the Negative Reciprocal Road is perpendicular to Smith Ave., then the line will be vertical because the Smith Ave line is horizontal. So, the perpendicular line that passes through (-14,2) is x = -14.

Hence, the equation that describes the Negative Reciprocal Road is x = -14.

(b)

First, we find the slope of Market Blvd using the points (6,6) and (7,0).

`m=(y_2-y_1)/(x_2-x_1)=(0-6)/(7-6)=-(6)/(1)=-6`

Then, we use the point-slope formula to find the Slope Street equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-6=-6(x-6) \\ y-6=-6x+36 \\ y=-6x+36+6 \\ y=-6x+42 \end{gathered}`

Hence, the equation of Slope Street is y = -6x + 42.