Question

At 94°F, a certain insect chirps at a rate of 60 times per minute, and at 96°F, they chirp 66 times per minute. Write an equation in slope-intercept form that represents the situation.

Answer 1

Explanation:

Let " x " denotes the temperature in degree Fahrenheit .

Let " y " denotes the chirp rate per minute .

We have given that at 94 degree Fahrenheit , chirp rate is 64 times per minute and at 96 degree Fahrenheit , it is 118 times per minute .

We write this information in coordinate form ( x,y) .

We have ( x₁ ,y₁) = ( 94 , 60 ) and ( x₂ , y₂) = ( 96,66) .

y₂ - y ₁ 66 - 60 6

Slope , m = ---------------------- = --------------------- = -----------

x₂ - x₁ 96 - 94 2

Slope , m = 6/2 = 3 .

Equation of line in slope intercept form is

y = m x + b where ' m' is slope and ' b ' is intercept .

Plug value of m , we get

y = 3 x + b .

To find value of b , we put ( 94 , 60 ) in place of x and y .

Put x = 94 and y = 60 , we get

60 = 3 * 94 + b

60 = 282 + b

60 - 282 = b

- 222 = b

Thus we get b = - 222 .

So the equation become

y = 3 x - 222 .

Equation in slope intercept form representing the situation is

y = 3 x - 222

Answer 2

`(x_1 = 94 , y_1 = 60)`

`(x_2 =96 ,y_2 = 66)`

And we can estimate the slope with the following formula:

`m =(y_2 -y_1)/(x_2 -x_1)= (66-60)/(96-94)=3`

And we can find the intercept using the first point given for example:

`60 = 3*94 +b`

And solving for b we got:

`b = 60 -282 = -222`

And the model would be given by:

`y = 3x -222`

Explanation:

For this case we can assume that the interest is find an equation for the times per minute with the temperature. So then the independent variable (x) would be the temperature and the dependent (y) the times per minute. We want to adjust a linera model like this one:

`y = mx +b`

We have the following info given:

`(x_1 = 94 , y_1 = 60)`

`(x_2 =96 ,y_2 = 66)`

And we can estimate the slope with the following formula:

`m =(y_2 -y_1)/(x_2 -x_1)= (66-60)/(96-94)=3`

And we can find the intercept using the first point given for example:

`60 = 3*94 +b`

And solving for b we got:

`b = 60 -282 = -222`

And the model would be given by:

`y = 3x -222`