Question

A real-world situation that can be modeled by the equation (y = 1/2x + 5).

(A) The height of a bouncing ball over time
(B) The temperature change over the course of a day
(C) The cost of a taxi ride based on distance
(D) The population growth of a city

Answer 1

The cost of a taxi ride based on distance can be modeled by the equation y = ½x + 5, representing a situation where the total cost ('y') increases by a constant rate per unit distance ('x') plus a base fare.

Step-by-step explanation:

The equation y = ½x + 5 can represent a linear relationship where 'y' is the dependent variable and 'x' is the independent variable. Each option given represents a different context in which this kind of linear relationship may be relevant. However, the most fitting real-world situation that can be modeled by this equation is (C) The cost of a taxi ride based on distance. This is because taxi fares often start with a base rate (which would be the y-intercept, or '5' in this case) and then increase at a constant rate per unit distance (the slope, '½' in this case). Therefore, 'y' could represent the total cost of the taxi ride, and 'x' could represent the number of units of distance traveled.