Use the image to answer the question.
Four lines and two points are graphed on a coordinate plane. The x-axis is labeled Hours and ranges from 0 to 2 in increments of 0.5. The y-axis is labeled Miles and ranges from 0 to 6 in increments of 2.
Bethany, Morgan, and Taylor all go to the local activity center after school. Each girl uses a different form of transportation to travel the six miles from the school to the activity center. Bethany walks, Morgan rides her bike, and Taylor takes the bus. Bethany leaves directly after school, and her distance can be modeled by the equation y=4x. Morgan leaves half an hour after Bethany, and her distance can be modeled by the equation y=8x−4. Taylor leaves one hour after Bethany, and her distance can be modeled by the equation y=20x−20. Use the linear function graph. Which girl arrives at the activity center first?
(1 point)
Responses
Morgan
Morgan
Taylor
Taylor
Bethany
Bethany
The girls all arrive at the same time.
To determine which girl arrives at the activity center first, we need to find the point where each of their respective lines intersects the y-axis. The y-intercept represents the distance each girl has traveled at time 0 (i.e., when they leave the school).
For Bethany, the equation is y = 4x. Plugging in x = 0, we find that y = 4(0) = 0. Therefore, Bethany has traveled 0 miles when she leaves the school.
For Morgan, the equation is y = 8x - 4. Plugging in x = 0, we find that y = 8(0) - 4 = -4. Therefore, Morgan has traveled -4 miles when she leaves the school. Since distance cannot be negative, we can conclude that Morgan has not left the school yet at x = 0.
For Taylor, the equation is y = 20x - 20. Plugging in x = 0, we find that y = 20(0) - 20 = -20. Therefore, Taylor has traveled -20 miles when she leaves the school. Since distance cannot be negative, we can conclude that Taylor has not left the school yet at x = 0.
Based on the y-intercepts, we can see that Bethany has traveled the least distance when she leaves the school, making her the first to arrive at the activity center.
Therefore, the girl who arrives at the activity center first is Bethany.