Question

a function, whose equation is $y = 6 + 3x$, represents the correlation between the number of hours that a plant is kept in the sunlight ($x$ hours) and the corresponding height ($y$ millimeters), to which it grows. what does the slope of this function represent and what are its units? \bigcirc the original height of the plant is 3 mm, and the units are mm. \bigcirc the original height of the plant is 6 mm, and the units are mm. \bigcirc the height of the plant increases 6 mm for every hour in the sunlight, and the units are mm/hr. \bigcirc the height of the plant increases 3 mm for every hour in the sunlight, and the units are mm/hr.

Explanation:

The function is in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. In the equation \( y=6 + 3x \), the slope \( m = 3 \). The slope represents the rate of change of \( y \) with respect to \( x \). Here, \( y \) is the height of the plant (in millimeters) and \( x \) is the number of hours in sunlight. So the slope represents the increase in height per hour of sunlight. The units of the slope are the units of \( y \) divided by the units of \( x \), which is \( \text{mm/hour} \) (or \( \text{mm/hr} \)).

Now let's analyze each option:

• Option 1: The original height (y - intercept) is 6, not 3, so this is wrong.
• Option 2: This describes the y - intercept (original height), not the slope, so this is wrong.
• Option 3: The slope is 3, not 6, so this is wrong.
• Option 4: The slope is 3, which means the height of the plant increases 3 mm for every hour in the sunlight, and the units are mm/hr. This matches our analysis.

Answer:

The height of the plant increases 3 mm for every hour in the sunlight, and the units are mm/hr. (The corresponding option description: The height of the plant increases 3 mm for every hour in the sunlight, and the units are mm/hr.)