Question

jack decides to coast to a stop on his bicycle, so he quits pedaling. the table represents his velocity (in meters per second) as a function of time (in seconds). what is the significance of the y - intercept?
a the number of seconds that jack coasted.
b the meters traveled after jack stopped pedaling.
c the meters traveled before jack stopped pedaling.
d the velocity of the bike when jack stopped pedaling.

Explanation:

In a function \(y = f(x)\), the \(y\)-intercept occurs when \(x = 0\). Here, \(x\) represents time (in seconds) and \(y\) represents velocity (in meters per second). When \(x = 0\) (the moment Jack stopped pedaling), the \(y\)-value (12) represents the velocity at that exact time.

• Option A: The number of seconds Jack coasted would be related to the \(x\)-values (time), not the \(y\)-intercept.
• Option B: Meters traveled is related to the area under a velocity - time graph (using integration for non - linear or sum for linear approximations), not the \(y\)-intercept.
• Option C: Since \(x = 0\) is when Jack stopped pedaling, it has nothing to do with the distance traveled before he stopped pedaling.
• Option D: When \(x = 0\) (the start of the coasting period, i.e., when he stopped pedaling), the \(y\)-value (velocity) is given by the \(y\)-intercept.

Answer:

D. The velocity of the bike when Jack stopped pedaling.