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
Bethany
Morgan
Taylor
The girls all arrive at the same time.
To find out which girl arrives at the activity center first, we need to look at the y-intercept of each equation. The y-intercept represents the distance each girl starts from. The girl with the smallest starting distance will arrive first.
For Bethany:
y = 4x
Her starting distance is y = 0 when x = 0.
So, Bethany starts at a distance of 0 miles.
For Morgan:
y = 8x - 4
Her starting distance is y = -4 when x = 0.
So, Morgan starts at a distance of -4 miles.
For Taylor:
y = 20x - 20
Her starting distance is y = -20 when x = 0.
So, Taylor starts at a distance of -20 miles.
Bethany has the smallest starting distance, so she arrives at the activity center first. Therefore, the answer is Bethany.