Question

the table shows the temperature of a greenhouse where the temperature was taken after x hours.
greenhouse temperature

hour, x	temperature (°f), y
5	60
8	66
9	68
13	76
15	80

when these data are graphed on a coordinate grid, the points all lie on the same line.
complete the statements below about the data by selecting the correct choice from each drop - down menu.

• the initial value, or y - intercept, of the linear function is 50 and represents the starting temperature in the greenhouse.
• the rate of change is 2 and represents drop - down menu.

Explanation:

To determine the rate of change (slope) of the linear function, we use the formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points from the table, e.g., \( (0, 50) \) and \( (5, 60) \).

Step 1: Calculate the slope

Using the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \), substitute \( x_1 = 0, y_1 = 50, x_2 = 5, y_2 = 60 \):

$$ m=\frac{60 - 50}{5 - 0}=\frac{10}{5} = 2 $$

Step 2: Interpret the rate of change

The rate of change (slope) of a linear function representing temperature over time (hours) tells us how much the temperature changes per hour. Since the slope is 2, it means the temperature in the greenhouse increases by 2°F per hour.

For the drop - down menu for what the rate of change represents, the correct option should be "the increase in temperature (in °F) per hour in the greenhouse".

Final Answer for the rate of change interpretation:

the increase in temperature (in °F) per hour in the greenhouse

Answer:

To determine the rate of change (slope) of the linear function, we use the formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points from the table, e.g., \( (0, 50) \) and \( (5, 60) \).

Step 1: Calculate the slope

Using the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \), substitute \( x_1 = 0, y_1 = 50, x_2 = 5, y_2 = 60 \):

$$ m=\frac{60 - 50}{5 - 0}=\frac{10}{5} = 2 $$

Step 2: Interpret the rate of change

The rate of change (slope) of a linear function representing temperature over time (hours) tells us how much the temperature changes per hour. Since the slope is 2, it means the temperature in the greenhouse increases by 2°F per hour.

For the drop - down menu for what the rate of change represents, the correct option should be "the increase in temperature (in °F) per hour in the greenhouse".

Final Answer for the rate of change interpretation:

the increase in temperature (in °F) per hour in the greenhouse