Question

which one of the following scenarios can be modeled by a linear function? (1 point)
the total number of students in a classroom.
the total number of fish caught on a fishing trip.
the total distance traveled at a speed of 55 miles per hour.
the total number of apples picked on any given day at a farm that allows you to pick your own apples.
graphing calculator

Explanation:

A linear function has a constant rate of change. Let's analyze each option:

• For "The total number of students in a classroom", the number of students is a fixed quantity (or changes in non - linear, discrete ways like adding a class, not a constant rate), so it's not linear.
• For "The total number of fish caught on a fishing trip", the number of fish caught can vary randomly (e.g., sometimes many, sometimes few, no constant rate of increase), so it's not linear.
• For "The total distance traveled at a speed of 55 miles per hour", the formula for distance is \(d = vt\) (where \(v = 55\) mph, a constant, and \(t\) is time). So the distance \(d\) changes at a constant rate (55 miles per hour) with respect to time \(t\), which is a linear relationship (in the form \(y=mx + b\), here \(b = 0\), \(m = 55\)).
• For "The total number of apples picked on any given day at a farm that allows you to pick your own apples", the number of apples picked can vary based on many factors (e.g., how many people pick, their speed which may not be constant), so it's not a linear relationship.

Answer:

C. The total distance traveled at a speed of 55 miles per hour.