To predict how many hot cocoas Dylan would sell at a temperature of 25°F using the line of best fit in the graph, we first need to identify the trend or equation of that line.

Observations from the graph:

• Two points on the line of best fit are clearly marked:
  • (0, 104) when the temperature is 0°F, 104 hot cocoas are sold.
  • (10, 96) when the temperature is 10°F, 96 hot cocoas are sold.

Finding the equation of the line:

The equation of a line can be expressed as:

$y = mx + b$

Where:

• $m$ is the slope,
• $b$ is the y-intercept.

Step 1: Calculate the slope $m$

The slope is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the points (0, 104) and (10, 96):

$m = \frac{96 - 104}{10 - 0} = \frac{-8}{10} = -0.8$

Step 2: Write the equation of the line

We know the y-intercept $b = 104$ (since when $x = 0$, $y = 104$).

Thus, the equation of the line is:

$y = -0.8x + 104$

Step 3: Predict for $x = 25$ (temperature 25°F)

Substitute $x = 25$ into the equation:

$y = -0.8(25) + 104 = -20 + 104 = 84$

So, based on the line of best fit, Dylan would sell 84 hot cocoas if the temperature were 25°F.

Would you like more details or have any further questions?

Here are 5 questions to expand on this:

1. How does the slope of a line relate to real-world situations like this one?
2. What happens to the number of hot cocoas sold as the temperature increases?
3. How do you determine the line of best fit if the points aren't as clear?
4. Could external factors besides temperature affect the number of cocoas sold? What could they be?
5. Why is it useful to make predictions based on a line of best fit?

Tip: Always double-check your slope calculation to ensure you're applying the correct rate of change.