1. **State the problem:** We want to find how many times a cricket will chirp per minute if the temperature outside is 57°F, based on the line of best fit from the given data.
2. **Identify the relationship:** The line of best fit shows a positive linear relationship between temperature ($y$) and chirps per minute ($x$). The points given are (60,51), (64,52), (68,53), (72,54), (76,55), and (80,56).
3. **Find the slope of the line:** The temperature increases by 1°F for every 4 chirps per minute. So the slope $m$ is:
$$m = \frac{\Delta y}{\Delta x} = \frac{1}{4}$$
4. **Write the equation of the line:** Using point-slope form with point (60,51):
$$y - 51 = \frac{1}{4}(x - 60)$$
5. **Rewrite in terms of $y$:**
$$y = \frac{1}{4}x - \frac{1}{4} \times 60 + 51 = \frac{1}{4}x - 15 + 51 = \frac{1}{4}x + 36$$
6. **Find chirps per minute for $y=57$:** Substitute $y=57$ and solve for $x$:
$$57 = \frac{1}{4}x + 36$$
7. **Isolate $x$:**
$$57 - 36 = \frac{1}{4}x$$
$$21 = \frac{1}{4}x$$
8. **Multiply both sides by 4:**
$$4 \times 21 = 4 \times \frac{1}{4}x$$
$$84 = \cancel{4} \times 21 = \cancel{4} \times \frac{1}{4}x = x$$
9. **Final answer:** The cricket would most likely chirp **84 times per minute** at 57°F.
Chirps Temperature E8926A
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