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 find out when Ella catches up with her mother, we need to look for the two lines that represent their respective distances over time.

Brandi's distance is represented by the equation \( y = 4x \) which indicates her distance in miles after \( x \) hours. Ella's distance is represented by the equation \( y = 6x - 12 \), which accounts for the two-hour delay in her start.

To determine when Ella catches up with Brandi, we need to find the intersection point of these two lines, as this point represents the same distance (y) at the same time (x) for both Brandi and Ella.

Now, let's analyze the options given:

• Option #1: Line 1 and Line 2 - This option is likely referring to Brandi's and Ella's lines.
• Option #2: Line 2 and Line 3 - This does not appear to correspond to Brandi and Ella's lines.
• Option #3: Line 3 and Line 4 - This seems irrelevant to our needs.
• Option #4: Line 1 and Line 4 - Unlikely to represent our situation either.

Since the problem describes that Brandi's line is \( y = 4x \) (let's assume this is Line 1) and Ella's is \( y = 6x - 12 \) (let’s assume this is Line 2), the intersection of Line 1 and Line 2 will show when Ella catches up with her mother.

Thus, the lines in option #1 can be used to determine when Ella catches up with her mother.

So, the answer is: Option #1: Line 1 and Line 2.