Final answer:
The linear equation that models the temperature as a function of the number of chirps per minute, use the formula for the slope of a line and substitute one of the points to find the y-intercept. The slope of the graph represents the rate at which the temperature increases with the number of chirps per minute.
Step-by-step explanation:
(a) Finding the linear equation:
To find a linear equation that models the temperature T as a function of the number of chirps per minute N, we first need to determine the slope (m) and y-intercept (b) of the equation. Given that a cricket produces 113 chirps per minute at 70°F and 183 chirps per minute at 80°F, we can use the formula for the slope of a line, which is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Using the points (70, 113) and (80, 183), the slope (m) is (183-113) / (80-70) = 7 chirps per °F. The y-intercept (b) can be found by substituting one of the points into the equation y = mx + b. Let's use the point (70, 113): 113 = 7 * 70 + b. Solving for b, we get b = -329.
Therefore, the linear equation that models the temperature T as a function of the number of chirps per minute N is T = 7N - 329.
(b) Slope interpretation:
The slope of the graph is 7. This means that for every increase of 1 chirp per minute, the temperature increases by 7°F. The slope represents the rate at which temperature increases as the number of cricket chirps per minute increases.
(c) Estimating the temperature:
To estimate the temperature when the crickets are chirping at 110 chirps per minute, we can substitute the chirping rate (N) into the linear equation and solve for T. T = 7(110) - 329 = 77°F (rounded to the nearest whole number).