a researcher studied the relationship between the number of times a certain species of cricket will chirp in…

a researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. her data is expressed in the scatter plot and line of best fit below. based on the line of best fit, how many times would the cricket most likely chirp per minute if the temperature outside were 68°f?

a researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. her data is expressed in the scatter plot and line of best fit below. based on the line of best fit, how many times would the cricket most likely chirp per minute if the temperature outside were 68°f?

Answer

Explanation:

Step1: Find the slope of the line

We use two - points on the line ((x_1,y_1)=(60,56)) and ((x_2,y_2)=(70,59)). The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). So (m=\frac{59 - 56}{70 - 60}=\frac{3}{10}=0.3).

Step2: Find the y - intercept of the line

We use the point - slope form (y - y_1=m(x - x_1)) with the point ((60,56)) and (m = 0.3). (y-56=0.3(x - 60)), expand to get (y-56=0.3x-18), then (y=0.3x + 38).

Step3: Predict the number of chirps

We want to find (x) when (y = 68). Substitute (y = 68) into the equation (y=0.3x + 38). So (68=0.3x+38). Subtract 38 from both sides: (68 - 38=0.3x), which gives (30 = 0.3x). Then divide both sides by 0.3: (x=\frac{30}{0.3}=100).

Answer:

100