Question

Jen has a map of a local park that is represented on a coordinate grid. There are several paths for walking and bicycling that extend the entire length of the park.

Jen is walking on a path that is represented on the map as a line with the equation y=2x+5
.
Her friend Dave is on a bike path that is represented on the map as a line with the equation y=0.5x+6.5
.
Which statement about Jen's path and Dave's path is true?

A.
The two paths are the same.

B.
The two paths will intersect at two different points.

C.
The two paths will intersect at one point.

D.
The two paths will never intersect.

Answer 1

To determine the relationship between Jen's path (represented by the equation \( y = 2x + 5 \)) and Dave's path (represented by the equation \( y = 0.5x + 6.5 \)), we can analyze their slopes.

1. **Identify the slopes of both lines**:
- Jen's path: The slope is \( 2 \).
- Dave's path: The slope is \( 0.5 \).

2. **Comparing the slopes**:
- Since \( 2 \) (Jen's slope) is not equal to \( 0.5 \) (Dave's slope), the two lines are not parallel and will therefore intersect.

3. **Determine the number of points of intersection**:
- Since they are not parallel and they are both linear equations (straight lines), they will intersect at exactly one point.

Based on this analysis, the correct answer is:

**C. The two paths will intersect at one point.**