Question

The following table shows the distance from school as a function of time:

Time (in minutes)
x Distance (in meters)
f(x)
0 36
3 32
6 28
9 24
12 20


Find and interpret the meaning of the x‐intercept in this scenario.
(36, 0); the distance away from the school
(27, 0); the time it takes to reach the school
(36, 0); the time it takes to reach the school
(27, 0); the distance away from the school

Answer 1

The x-intercept (27, 0) represents the time it takes the student to reach the school, which is 27 minutes based on the given rate of movement towards the school.

Step-by-step explanation:

The x-intercept in a graph represents the point where the line crosses the x-axis, which is where the value of the function (distance in this case) is zero. In the context of this scenario, the x-intercept would represent the time when the student's distance from school reaches zero, meaning they have arrived at school.

To find the x-intercept, we would look at the pattern in the table and extrapolate from there.

Since the student is moving 4 meters closer to school every 3 minutes, we can calculate the x-intercept by setting the function to zero and solving for x.

Given that it starts at 36 meters away and closes in 4 meters every 3 minutes, the time it would take to reach the school can be calculated by dividing the initial distance by the rate of change per minute.

To interpret the x-intercept, we divide the initial distance (36 meters) by the rate at which the distance decreases every minute (4 meters every 3 minutes). This gives us:

`\[\frac{36 \text{ meters}}{\frac{4 \text{ meters}}{3 \text{ minutes}}} = 27 \text{ minutes}\]`

Thus, the x-intercept is (27, 0), and it represents the time it takes to reach the school. This means that in the context of this problem, the student takes 27 minutes to reach the school from their starting distance.