Question

At 110°F, a certain insect chirps at a rate of 103 times per minute, and at 115°F, they chirp 143 times per minute. Write an equation in slope-intercept form that represents the situation.

A) y = 2x + 23
B) y = 4x - 327
C) y = 20x + 83
D) y = 2x - 77

Answer 1

The equation that represents the situation is y = 2x - 77.

Step-by-step explanation:

The given problem involves finding a linear equation in slope-intercept form that represents the relationship between temperature (T) and the chirping rate (y) of a certain insect. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.

To find the equation, we can use the given data points. At 110°F, the chirping rate is 103 times per minute, which gives us the point (110, 103). At 115°F, the chirping rate is 143 times per minute, which gives us the point (115, 143).

Using the two points, we can calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (143 - 103) / (115 - 110) = 40 / 5 = 8.

Now that we have the slope, we can substitute one of the points and the slope into the slope-intercept form equation to find the y-intercept (b). Using the point (110, 103) and the slope m = 8, we can solve for b:

103 = 8(110) + b

103 = 880 + b

b = -777.

Therefore, the equation that represents the situation is y = 8x - 777, or in slope-intercept form, answer D) y = 2x - 77.