Question

At 82°F, a certain insect chirps at a rate of 61 times per minute, and at 91°F, they chirp 124 times per minute. Write an equation in slope-intercept form that represents the situation.

Answer 1

`y=7x-513`

Explanation:

Let

x----> the temperature in degrees Fahrenheit

y ---->insect chirping rate in times per minute

we have the ordered pairs

(82,61) and (91,124)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(124-61)/(91-82)`

`m=(63)/(9)=7`

step 2

Find the equation of the line

we know that

The equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-intercept

we have

`m=7` ---> the units are chirps per minute/degree F

take the point (82,61)

substitute and solve for b

`61=7(82)+b`

`61=574+b`

`b=-513`

substitute

`y=7x-513`