# 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 al the point (4, 5). Write an equation that represents the path.

Question
Modeling data distributions
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 al the point $$\displaystyle{\left({4},\ {5}\right)}.$$ Write an equation that represents the path.

2021-03-08
Calculation:
As the given in the figure the railroad track and passes through the points $$\displaystyle{\left({11},\ {4}\right)}$$ and $$\displaystyle{\left({8},\ {0}\right)}.$$ Therefore slope is $$\displaystyle{\frac{{{0}-{4}}}{{{8}-{11}}}}={\frac{{-{4}}}{{-{3}}}}={\frac{{{4}}}{{{3}}}}.$$
As the new bike path is parallel to rail road track so slope are equal. Slope of new bike path is $$\displaystyle{\frac{{{4}}}{{{3}}}}.$$
Equation of new bike path is:
$$\displaystyle{y}-{5}={\frac{{{4}}}{{{3}}}}{\left({x}-{4}\right)}$$
$$\displaystyle{3}{y}-{15}={4}{x}-{16}$$
$$\displaystyle{4}{x}-{3}{y}={16}-{15}$$
$$\displaystyle{4}{x}-{3}{y}={1}$$
Thus, equation of the bike path is $$\displaystyle{4}{x}\ -\ {3}{y}={1}.$$

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