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]
Read more about equations of straight line at:
https://brainly.com/question/21627259
