Exercise 29 Page 184

Remember that equations written in point-slope form follow a specific format. y- y_1= m(x- x_1) In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. In our case, let x represents the number of chirps and y the temperature. We know that when the temperature is 50^(∘) F a cricket chirps 40 times, this can be rewritten as a ordered pair. (Chirps,Temperature) → (40,50) For each rise in temperature of 0.25 ^(∘) F, the cricket makes and additional chirp each minute. Then, another ordered point can be (41,50.25) which represents the number of chirps when the temperature is 50.25^(∘) F. Now that we have two points, let's determine the slope with the slope formula.

Now that we know the slope is 0.25, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 40, 50).

This equation represents the temperature per number of chirps. We want to find the temperature if we count 100 chirps in 1 minute. To do so, let's substitute x= 100 into the obtained equation.

The temperature is 65^(∘) F when we count 100 chirps per minute.