Subjects algebra

Chirps Temperature E8926A

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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.