To interpret the slope and y-intercept of the linear model for ice cream sales based on temperature, let's define the elements involved:
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Y-Intercept (0, 38): This point represents the estimated number of ice cream sales when the temperature is 0°F. Specifically, the y-intercept here is 38, meaning that when the temperature is at the absolute zero mark (which is quite unrealistic in this context, but mathematically valid), it is estimated that there would be 38 units of ice cream sold.
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Slope: The slope of the linear model indicates how much ice cream sales change for each one-degree increase in temperature. If you have a specific ordered pair given as (65, 325), this means that at a temperature of 65°F, there are 325 units sold.
To find the slope, we can use the general formula for the slope between two points, which is:
\[ \text{slope} = \frac{y2 - y1}{x2 - x1} \]
Assuming you provide us with two points (0, 38) and (65, 325), we can calculate the slope:
- Here, \((x1, y1) = (0, 38)\) and \((x2, y2) = (65, 325)\).
Applying the values:
\[ \text{slope} = \frac{325 - 38}{65 - 0} = \frac{287}{65} \approx 4.41 \]
So, the slope rounds to 4.41, meaning for each additional degree Fahrenheit in temperature, ice cream sales increase by approximately 4.41 units.
Summary Interpretation:
- Y-Intercept (0, 38): At 0°F, ice cream sales are predicted to be 38 units.
- Slope (4.41): For each 1°F increase in temperature, ice cream sales are predicted to increase by about 4.41 units.