Question

Which situation can be modeled by the equation y = mx + b?

Answer 1

We have to check which of the statements can be modeled as y = mx + b. This equation represents a straight line or is a linear equation. Hence, in the given options we will check which statement represents a linear equation.

Statement A: The number of bacterial cells (y) in a Petri dish doubles every hour (x).  

This can be expressed as y (x) = y (x-1) * 2, which is not a linear function. Refer attached image

Statement B: The time (y) it takes to fill an 80-gallon bathtub depends on the number of gallons filled per minute (x).

Here, we can not determine the expression and we just know that the time (y) is a function of number of gallons filled per minute (x).

Statement C: The total cost (y) of publishing a textbook at a printing cost of $9.50 per book depends on the number of books (x) published.  

This can be expressed as y = 9.5 * x. This is a linear function, which will grow by a factor of 9.5 with each unit change in x. Refer attached image.

Statement D: The volume (y) of a conical flask with a height of 6 inches depends on the radius (x) of the flask.

Here, we can not determine the expression, but we know that the volume of a cone with 6 inch height is a function of the cone's radius.

Hence, statement C can be modeled by the equation y = mx + b.