Question

At 79°F, a certain insect chirps at a rate of 104 times per minute, and at 82°F, they chirp 128 times per minute. Write an equation in slope-intercept form that represents the situation?

Answer 1

The slope-intercept form equation representing the insect chirping rate as a function of temperature is C = 8T - 528, where C represents the chirping rate per minute and T represents the temperature in degrees Fahrenheit.

Step-by-step explanation:

To write an equation in slope-intercept form that represents the insect chirping rate as a function of temperature, we can use the given data points: (79°F, 104 chirps/minute) and (82°F, 128 chirps/minute). The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

First, we determine the slope, m, which is the change in chirp rate over the change in temperature. The slope m is calculated as:

m = (Change in chirping rate) / (Change in temperature) = (128 chirps/minute - 104 chirps/minute) / (82°F - 79°F) = 24 chirps/minute / 3°F = 8 chirps/minute/°F

Next, we find the y-intercept, b. We can use either of the given points. For example, when Temperature (T) = 79°F, Chirping rate (C) = 104 chirps/minute, we get:

104 = (8)(79) + b
b = 104 - (8)(79)
b = 104 - 632
b = -528

So the final equation representing the situation in slope-intercept form is:

C = 8T - 528

Where C is the chirping rate in chirps/minute and T is the temperature in degrees Fahrenheit.