Scatter Plots & Data Analysis Online Practice

Question

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Question
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An illustration shows the first quadrant of a coordinate plane titled Temperature Fahrenheit vs Ice Cream Sales.
The x-axis shows temperature in degrees Fahrenheit and ranges from 0 to 85 in increments of 5. The y-axis shows sales in dollars and ranges from 0 to 500 in increments of 50. Eight points are plotted on the graph. The points are plotted at approximate coordinates left parenthesis 0 comma 100 right parenthesis, left parenthesis 50 comma 180 right parenthesis, left parenthesis 55 comma 210 right parenthesis, left parenthesis 60 comma 230 right parenthesis, left parenthesis 65 comma 350 right parenthesis, left parenthesis 70 comma 70 right parenthesis, left parenthesis 70 comma 375 right parenthesis, and left parenthesis 80 comma 500 right parenthesis. An upward slanting line starts at left parenthesis 0 comma 40 right parenthesis and continues to left parenthesis 65 comma 325 right parenthesis.

Market data are gathered for ice cream sales based on the temperature in Fahrenheit. Interpret the slope and y-intercept (0,38)
of the linear model, using the ordered pair (65,325)
. Round the slope to the nearest hundredth.

(1 point)
Responses

For every degree increase in temperature, ice cream sales increase $4.42.
For every degree increase in temperature, ice cream sales increase $4.42.

For every degree increase in temperature, ice cream sales increase $4.40.
For every degree increase in temperature, ice cream sales increase $4.40.

For every 4.42 increase in temperature, ice cream sales increase $1.
For every 4.42 increase in temperature, ice cream sales increase $1.

For every degree increase in temperature, ice cream sales increase $0.23.

Answer 1

To analyze the linear model and interpret the slope and y-intercept, we first need to determine the slope of the line.

The slope \( m \) of a line can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (0, 38) and (65, 325):

• \( x_1 = 0 \), \( y_1 = 38 \)
• \( x_2 = 65 \), \( y_2 = 325 \)

Substituting these values into the slope formula:

\[ m = \frac{325 - 38}{65 - 0} = \frac{287}{65} \approx 4.42 \]

Now, interpreting the values:

• Slope \( m \approx 4.42 \): This means for every degree increase in temperature, ice cream sales increase approximately $4.42.
• Y-intercept (0, 38): This indicates that when the temperature is 0 degrees Fahrenheit, ice cream sales are approximately $38.

Given the options provided:

• For every degree increase in temperature, ice cream sales increase $4.42.

This response correctly interprets the slope of the line.

So, the correct answer is:

For every degree increase in temperature, ice cream sales increase $4.42.