Question

A parks and recreation department is constructing a new bike path the path will be parallel to the railroad tracks shown and pass through the parking area at the point (4,5). write an equation that represents the path Graph the equation you created on below to show where the new bike path will be parallel to the railroad track.

Answer 1

First let's calculate the slope of the curve

A = (8,0)

B = (11,4)

$\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{4-0}{11-8} \\ m=\frac{4}{3} \\ \end{gathered}$

A straight line parallel to that curve has the same slope

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

m = 4/3

Now, what about b, the y-intercept?

$\begin{gathered} b=y-mx \\ b=5-\frac{4}{3}\cdot4 \\ b=5-\frac{16}{3}_{} \\ b=-\frac{1}{3} \end{gathered}$

The equation of the line that passes through the point (4,5) with a slope of 4/3

$y=\frac{4}{3}x-\frac{1}{3}_{}$

Blue line is the new bike path

Red line is the railroad