Question

Errol's bike ride from home to school can be modeled by the equation d(t) = -4t+2, where d(t) is

his distance from school, in miles, at t minutes. Errol's friend Daniel lives 4 miles away from school. It
takes Daniel twice as long to get to school if he bike rides at the same pace as Errol. What can be said
about the graph of the equation that models Daniel's bike rides?

Answer 1

Option (2).It has a vertical translation by 2 units in the positive direction.

Explanation:

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Errol's bike ride can be modeled by the equation,

`d(t)=-(1)/(4)t+2`

Slope of the given equation =
`-(1)/(4)` which shows the rate of change of distance from Errol's house

Y-intercept = 2, shows the distance of the school from Errol's house

Let the equation that represents the distance of Daniel's home from the school is,

y = mt + b

Since speed of Daniel is equal to the speed of Errol, slopes of both the equations will be same.

Since y-intercept 'b' represents the distance from his home, b = 4

Now the equation will be,

`d(t)=-(1)/(4)t+4`

Therefore, the graph representing the Daniel's equation will have a vertical translation by 2 units in the positive direction.