Question

At 88°F, a certain insect chirps at a rate of 64 times per minute, and at 97°F, they chirp 118 times per minute. Write an equation in slope-intercept form that represents the situation.

Answer 1

Let " x "  denotes the temperature in degree Fahrenheit .

Let  " y " denotes the chirp rate per minute .

We have given that at 88 degree Fahrenheit , chirp rate is 64 times per minute and at 97 degree Fahrenheit , it is 118 times per minute .

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

We have ( x₁ ,y₁)  = ( 88 , 64 )  and  ( x₂ , y₂) = ( 97,118) .

                         y₂   - y ₁                     118  -   64                  54

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

                          x₂  - x₁                        97   -  88                   9

           Slope , m =  6 .

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 = 6 x + b .

To find value of b , we put ( 88 , 64 ) in place of x and y .

Put x = 88 and y = 64 , we get

64 = 6 * 88 + b

64  = 528 + b

64 - 528 =  b

- 464 = b

Thus we get b = - 464 .

So the equation become

y = 6 x - 464 .

Equation in slope intercept form representing the situation is

y = 6 x - 464 .