Question

a hiking path is represented by the equation y=3/8x on a coordinate map. The county would like to create a parallel path for bikers. If the new path goes through the point (16,7), whats the equation of the bike path?

Answer 1

Answer:

The equation of the bike path on a coordinate map is represented by $y = \frac{3}{8}\cdot x +1$.

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:

$y-y_{o} = m_{\parallel}\cdot (x-x_{o})$

Where:

$x_{o}$, $y_{o}$ - Components of known point, dimensionless.

$m_{\parallel}$ - Slope of the parallel line, dimensionless.

In addition, a line has also this form:

$y = m\cdot x + b$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$m$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

Given that parent function is $y = \frac{3}{8}\cdot x$, the slope of the resulting line is $m_{\parallel} = \frac{3}{8}$. Now, if $x_{o} = 16$ and $y_{o} = 7$, we obtain the equation of the line:

$y-7 = \frac{3}{8}\cdot (x-16)$

$y = \frac{3}{8}\cdot x +1$

The equation of the bike path on a coordinate map is represented by $y = \frac{3}{8}\cdot x +1$.