Question

Use the image to answer the 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.
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The first line is dotted and is labeled Line 1. Line 1 passes through coordinates left parenthesis 3 comma 10 right parenthesis and left parenthesis 8 comma 20 right parenthesis. The second line is solid and is labeled Line 2. Line 2 passes through coordinates left parenthesis 2 comma 0 right parenthesis and left parenthesis 7 comma 30 right parenthesis. The third line is long dot-dashed and is labeled Line 3. Line 3 passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 20 right parenthesis.

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

The lines in option #2 can be used.

Line 3 is y = 4x (Brandi) and Line 2 is y = 6x − 12 (Ella).