Use the image to answer the question.

Question

Four lines are graphed on a coordinate plane. The x-axis is labeled Hours and ranges from 0 to 9 in increments of 1. The y-axis is labeled Miles and ranges from 0 to 40 in increments of 10.

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?

Option #1: Line 1 and Line 2

Option #2: Line 2 and Line 3

Option #3: Line 3 and Line 4

Option #4: Line 1 and Line 4

(1 point)
The lines in option #
can be used to determine when Ella catches up with her mother.

Answer 1

To determine when Ella catches up with her mother, we need to examine the equations of the lines that represent their distances over time.

Brandi's hiking distance is represented by the equation:

\[ y = 4x \]

Ella's hiking distance is given by the equation:

\[ y = 6x - 12 \]

To find the point where Ella catches up with Brandi, we need to set the distances equal to each other, which means we need to find the intersection of the two lines. Therefore, we should look for the lines corresponding to Brandi's distance (Line 1) and Ella's distance (Line 2).

Therefore, the correct option that can be used to determine when Ella catches up with her mother is:

Option #1: Line 1 and Line 2.