Biologists have found that the number of chirps some crickets make per minute is related to temperature. the relationship is very close to being linear. when crickets chirp 124 times a minute, it is about 68°f. when they chirp 172 times a minute, it is about 80°f. (a) find an equation for the line that models this situation; (b) how warm is it when the crickets are chirping 160 times a minute?

a) f(x) = 0.25x + 37

b) 77ºF

Step-by-step explanation:

a) The relation between chirps per minute and temperature is linear, therefore we know that f(x) = mx + b for some m and b. To find the equation that models this, we will need to find m and b.

From the data that the problem gives us we know that the independent variable x is the number of crickets per minute and the dependant variable is the temperature. We know will write down the equations and solve:

68 = 124m + b

80 = 172m + b.

Therefore the equation would be:

f(x) = 0.25x + 37

b) How warm is it when the crickets are chirping 160 times a minute?

f(160) = 0.25 (160) + 37

f(160) = 40 + 37

f(160) = 77

It will be 77ºF

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step-by-step explanation:

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)