Question

(04.02 mc)
a city planner is rerouting traffic in order to work on a stretch of road. the equation of the path of the old route can be described as ( y = \frac{2}{5}x - )

1. what should the equation of the new route be if it is to be parallel to the old route and will go through point ( (q, p) )?

( circ y - q = -\frac{5}{2}(x - p) )
( circ y - q = \frac{2}{5}(x - p) )
( circ y - p = \frac{5}{2}(x - q) )
( circ y - p = \frac{2}{5}(x - q) )

Explanation:

Step1: Identify slope of old route

The old route is $y=\frac{2}{5}x - 4$, so slope $m=\frac{2}{5}$.

Step2: Parallel lines have equal slopes

New route slope $m=\frac{2}{5}$.

Step3: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $(x_1,y_1)=(Q,P)$ and $m=\frac{2}{5}$.
<Expression>
$y-P=\frac{2}{5}(x-Q)$
</Expression>

Answer:

$\boldsymbol{y-P=\frac{2}{5}(x-Q)}$ (Option D)