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

Answer 1

y=4/3x-1/3 the slope matches the like parallel and allows it to pass through the point

Answer 2

Answer:

The equation of the bike path is : 4x - 3y = 1

Step-by-step explanation:

Coordinates of railway track: (8,0), (11,4)

Slope of the railway track:

Slope = m =$\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{4-0}{11-8}=\frac{4}{3}$

A parks and recreation department is constructing new bike path parallel to railroad tracks with point (4,5).

The slope of parallel lines are equal. So, the slope of line or bike path with point (4,5) will same as that of the slope of railroads tracks.

Slope of bike path = m' =  m = $\frac{4}{3}$

In order to determine the equation of bike path we we use point slope form:

$(y-y_1)=m\times (x-x_1)$

The equation of the bike path is:

$(y-5)=\frac{4}{3}\times (x-4)$

4x - 3y = 1