Question

theres a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside, as expressed in the graph below. what is the meaning of the x - value when y = 75?

Explanation:

Step1: Find two points on the line

From the graph, we can take two points \((x_1,y_1)=(200,40)\) and \((x_2,y_2)=(0,100)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values: \(m=\frac{100 - 40}{0 - 200}=\frac{60}{-200}=-\frac{3}{10}\)

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

Using the point \((x_1,y_1)=(200,40)\) and \(m =-\frac{3}{10}\), we get \(y - 40=-\frac{3}{10}(x - 200)\)

Step4: Simplify the equation

$$
LATEXBLOCK0
$$

Step5: Substitute \(y = 75\) into the equation

$$
LATEXBLOCK1
$$

Answer:

The \(x\) - value when \(y = 75\) is approximately \(83\) (rounded to the nearest whole number)