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:y=3/8x +1

Explanation:

Answer 2

The equation of the bike path on a coordinate map is represented by
`y = (3)/(8)\cdot x +1`.

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 = (3)/(8)\cdot x`, the slope of the resulting line is
`m_(\parallel) = (3)/(8)`. Now, if
`x_(o) = 16` and
`y_(o) = 7`, we obtain the equation of the line:

`y-7 = (3)/(8)\cdot (x-16)`

`y = (3)/(8)\cdot x +1`

The equation of the bike path on a coordinate map is represented by
`y = (3)/(8)\cdot x +1`.