Question

Jalynn and Emma enjoy hiking. Jalynn hikes 1 mile in 20 minutes. Emma hikes at a rate of 3 miles per hour. On Sunday at 8:00 a.m., they both left the trailhead. The line representing Jaylynn’s progress is graphed.

Jalynn's y=1/20x
Emma's y=3(1/60)x






Which statements are true about the system that models this scenario?

The lines will have equal slopes so there is no solution.

The equations are equivalent so there are an infinite number of solutions.

The equations have only one solution at (0, 0) since the hikers walk at different speeds.

Both lines will have a y-intercept of (0, 0) since both hikers start at 8:00 a.m.

As shown on the graph, both lines have a slope of 1/20 because one must convert to the same units of time.

Answer 1

The equations are equivalent so there are an infinite number of solutions.

Both lines will have a y-intercept of (0,0) since both hikers start at 8:00 a.m.

As shown on the graph, both lines have a slope of 1/20 because one must convert to the same units of time.

Explanation:

Answer 2

Explanation:

Jalynn hikes 1 mile in 20 minutes. This means that Jalynn's speed is 1/20 miles per minute. The slope is /20 miles per minute.

Emma hikes at a rate of 3 miles per hour. Since 1 hour = 60 minutes, Emma's speed is 3/60 = 1/20 miles per minute. The slope is also 1/20 miles per minute. The lines are parallel to each other because the slopes are equal.

Therefore, the statements following are true about the system that models this scenario.

1) The lines will have equal slopes so there is no solution.

2) The equations are equivalent so there are an infinite number of solutions.

4) Both lines will have a y-intercept of (0, 0) since both hikers start at 8:00 a.m.