Question

At 106°F, a certain insect chirps at a rate of 67 times per minute, and at 108°F, they chirp 83 times per minute. Write an equation in slope-intercept form that represents the situation.

Answer 1

`y=8x-781`

Here,
`x` represents temperature and
`y` denotes rate of chirping per minute.

Explanation:

Let
`x` represents temperature and
`y` denotes rate of chirping per minute.

At
`106`°F, a certain insect chirps at a rate of
`67` times per minute.

Take
`(x_1,y_1)=(106,67)`

At
`108`°F, they chirp
`83` times per minute.

Take
`(x_2,y_2)=(108,83)`

Slope intercept form:

`y-y_1=((y_2-y_1)/(x_2-x_1))(x-x_1)`

`y-67=((83-67)/(108-106))(x-106)\\\\y-67=((83-67)/(108-106))(x-106)\\\\y-67=((16)/(2))(x-106)\\\\y-67=8(x-106)\\y-67=8x-848\\y=8x+67-848\\y=8x-781`