Answer:
The equation of the bike path on a coordinate map is represented by [tex]y = \frac{3}{8}\cdot x +1[/tex].
Step-by-step explanation:
From Analytical Geometry, we know that resultant parallel line is a translated version of parent line. Two lines are parallel to each other when they share the same slope. The resultant line can be construted from slope-point form:
[tex]y-y_{o} = m_{\parallel}\cdot (x-x_{o})[/tex]
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Components of known point, dimensionless.
[tex]m_{\parallel}[/tex] - Slope of the parallel line, dimensionless.
In addition, a line has also this form:
[tex]y = m\cdot x + b[/tex]
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
Given that parent function is [tex]y = \frac{3}{8}\cdot x[/tex], the slope of the resulting line is [tex]m_{\parallel} = \frac{3}{8}[/tex]. Now, if [tex]x_{o} = 16[/tex] and [tex]y_{o} = 7[/tex], we obtain the equation of the line:
[tex]y-7 = \frac{3}{8}\cdot (x-16)[/tex]
[tex]y = \frac{3}{8}\cdot x +1[/tex]
The equation of the bike path on a coordinate map is represented by [tex]y = \frac{3}{8}\cdot x +1[/tex].
