Question

At 107 f, a certain insect chirps at a rate of 79 times per minute, and at 113*F, they chirp 91 times perminute Write an equation in slope-intercept form that represents the situation.

Answer 1

At 107 *F, a certain insect chirps at a rate of 79 times per minute, and at 113*F, they chirp 91 times per

minute.

Let x denotes the temperature values and y denotes the chirping rate.

`\begin{gathered} (x_1,y_1)=(107,79) \\ (x_2,y_2)=(113,91) \end{gathered}`

Recall that equation in the slope-intercept form is given by

`y=mx+b`

Where m is the slope and b is the y-intercept.

The slope is given by

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

Let us substitute the given points into the above slope formula.

`m=(y_2-y_1)/(x_2-x_1)=(91-79)/(113-107)=(12)/(6)=2`

So, the slope is 2

The equation becomes

`y=2x+b`

Now to find the y-intercept (b) substitute any one point into the above equation and solve for (b)

Let us choose (107, 79)

`\begin{gathered} y=2x+b \\ 79=2(107)+b \\ 79=214+b \\ 79-214=b \\ -135=b \\ b=-135 \end{gathered}`

So, the y-intercept is -135

Therefore, the equation in slope-intercept form is

`y=2x-135`