Question

The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 4 + 2x What does the slope of this function represent? A. The original height of the plant was four mm. B. The original height of the plant was two mm. C. The height of the plant increases by two mm for every hour of sunlight it receives. D. The height of the plant increases by four mm for every hour of sunlight it receives.

Answer 1

The slope of the function y = 4 + 2x represents the rate at which the height of the plant increases with respect to sunlight hours, which is 2 mm per hour. Therefore, the correct answer is that the plant's height increases by 2 mm for every additional hour of sunlight.

Step-by-step explanation:

The function in question is y = 4 + 2x, which can be understood through the general slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is the coefficient of the independent variable x, which is 2. This means that the height of the plant increases by 2 mm for each additional hour of sunlight. Therefore, the correct interpretation of the slope in this function is that for every one-unit increase in the independent variable (the number of hours of sunlight), the dependent variable (the plant height) increases by the slope value.

So, for this function, the slope represents the rate of growth of the plant with respect to the number of hours of sunlight received. The answer to the student's question is that option C is correct: The height of the plant increases by two mm for every hour of sunlight it receives.

Answer 2

C. its in the form y = mx + b where m is the slope