Brandi and her daughter, Ella, are training for a hiking challenge. Because Brandi hikes at a slower pace than her daughter, she begins the practice hike two hours earlier. If Brandi averages a pace of 4 mph, the linear equation y=4x can be used to model her distance, y, in miles with respect to her time, x, in hours. If Ella averages a pace of 6 mph and begins two hours after her mom, the linear equation y=6x-12 can be used to model her distance, y, in miles with respect to time, x, in hours. The graph of which two lines can be used to find the time and distance when Ella catches up with her mother?

Question

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(1 point)
Responses

Line 1 and Line 2
Line 1 and Line 2

Line 2 and Line 3
Line 2 and Line 3

Line 3 and Line 4
Line 3 and Line 4

Line 1 and Line 4

Answer 1

To find out when Ella catches up with her mother, we need to identify the two lines represented by their equations:

1. Brandi's distance as a function of time is modeled by the equation: \[ y = 4x \] where \( y \) is the distance in miles and \( x \) is the time in hours since Brandi started hiking.

2. Ella's distance is modeled by the equation: \[ y = 6x - 12 \] where \( y \) is her distance in miles, and \( x \) is the time in hours since Ella started hiking, which is two hours after Brandi.

To find out when Ella catches up with her mother, we are looking for the point where these two lines intersect — that is, when their distances are equal:

\[ 4x = 6x - 12 \]

Solving this equation will give the time \( x \) when Ella catches up. However, in the context of your question, you're simply looking for the correct lines to compare.

The two equations we have:

• Line 1: Brandi's distance \( y = 4x \)
• Line 2: Ella's distance \( y = 6x - 12 \)

Thus, the correct response indicating which lines can be used to find the time and distance when Ella catches up with her mother is:

Line 1 and Line 2