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

Parallel lines have the same slope
The equation of the bike path is: [tex]\mathbf{3y = 4x - 1}[/tex]
The points on the railroad tracks are:
(11,4) and (8,0)
The slope of these points is calculated as follows:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{0-4}{8 - 11}}[/tex]
[tex]\mathbf{m = \frac{-4}{- 3}}[/tex]
[tex]\mathbf{m = \frac{4}{3}}[/tex]
Since the bike path is parallel to the railroad track, then they will have the same slope
The point on the bike path is: (4,5)
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
This gives:
[tex]\mathbf{y = \frac 43(x - 4) + 5}[/tex]
Multiply through by 3
[tex]\mathbf{3y = 4(x - 4) + 15}[/tex]
Open bracket
[tex]\mathbf{3y = 4x - 16 + 15}[/tex]
[tex]\mathbf{3y = 4x - 1}[/tex]
Hence, the equation of the bike path is: [tex]\mathbf{3y = 4x - 1}[/tex]
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