Which situation can be modeled by the equation y = mx + b?
Select one:
a. The volume (y) of a cylindrical tank with a height of 2 feet depends on the radius (x) of the tank.
b. The total income (y) of a worker who earns 8 dollars per hour depends on the number of hours (x) worked.
c. The number of butterflies (y) in a population doubles every month (x).
d. The time (y) it takes a car to travel 100 miles depends on the speed (x) of the car.
a. but I see y = 2 * pi x^2 and x^2 is not x
b. y = 8 x + 0 well that is reasonable
c. y = x initial * 2^n heavens no
d. y = 100 / x well hardly
E
b. The total income (y) of a worker who earns 8 dollars per hour depends on the number of hours (x) worked.
The situation that can be modeled by the equation y = mx + b is option b: The total income (y) of a worker who earns 8 dollars per hour depends on the number of hours (x) worked.
To understand why, let's break down the equation y = mx + b:
- The variable y represents the dependent variable, which is the total income of the worker.
- The variable x represents the independent variable, which is the number of hours worked.
- The coefficient m represents the rate of change of the dependent variable with respect to the independent variable. In this case, the rate of change is 8 dollars per hour, as the worker earns 8 dollars for every hour worked.
- The constant term b represents the y-intercept, which is the value of y when x is equal to 0. In the context of this equation, it would represent a base income or any fixed income not dependant on the number of hours worked.
Therefore, the equation y = mx + b perfectly represents the situation described in option b.