Question

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 66°f? answer attempt 1 out of 2 chirps per minute submit answer

Explanation:

Step1: Find two points on the line of best fit

We have two points \((90,64)\) and \((93,65)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 90,y_1=64,x_2 = 93,y_2 = 65\)

$$m=\frac{65 - 64}{93 - 90}=\frac{1}{3}$$

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((90,64)\) and \(m=\frac{1}{3}\), the equation of the line is \(y-64=\frac{1}{3}(x - 90)\)

Step4: Simplify the equation

$$y-64=\frac{1}{3}x-30$$

$$y=\frac{1}{3}x + 34$$

Step5: Substitute \(y = 66\) (temperature) into the equation

$$66=\frac{1}{3}x+34$$

Step6: Solve for \(x\)

Subtract 34 from both sides: \(66 - 34=\frac{1}{3}x\)

$$32=\frac{1}{3}x$$

Multiply both sides by 3: \(x = 96\)

Answer:

\(66\)