Question

At 73°F a certain insect chirps at a rate of 97 times per minute, and at 80°F, they chirp 132 times per

minute. Write an equation in slope-intercept form that represents the situation.

Answer 1

The equation is: y = 5x - 268

Step-by-step explanation:

We are given that:

At 73°F, the chirp is 97 times per minute .........> first point is (73, 97)

At 80°F, the chirp is 132 times per minute .......> second point is (80, 132)

The general equation of the linear line is:

y = mx + c

where m is the slope and c is the y-intercept

1- getting the slope:

The slope can be calculated using the following rule:

`m = (y_2 - y_1)/(x_2 - x_1)`

Substitute with the given points to get the slope as follows:

`m = (132 - 97)/(80 - 73) = 5`

The equation, now, became:

y = 5x + c

2- getting the y-intercept:

To get the y-intercept, use any of the given points and substitute in the rule we got in part 1. I will use the point (80, 132)

Therefore:

y = 5x + c

132 = 5(80) + c

c = 132 - 5(80) = -268

The equation, therefore, is:

y = 5x - 268

Hope this helps :)