Question

when a cricket chirps 40 times in one minute, the temperature is about 50°f. when a cricket chirps 80 times in one minute, the temperature is about 60°f. the temperature in degrees fahrenheit, y, is a linear function of the number of chirps, x. points on the graph: (40, 50) and (80, 60) rate of change: \\(\frac{1}{4}\\) what is the temperature when there are no chirps at all? find the initial value. \\(\square\\)°f

Explanation:

Step1: Recall linear function form

A linear function is \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the initial value (y-intercept). We know \( m=\frac{1}{4} \), and we can use a point \((x,y)\) to find \( b \).

Step2: Substitute a point into the equation

Use the point \((40, 50)\) and \( m = \frac{1}{4} \) in \( y = mx + b \). So, \( 50=\frac{1}{4}(40)+b \).

Step3: Solve for \( b \)

Calculate \( \frac{1}{4}(40)=10 \). Then, \( 50 = 10 + b \). Subtract 10 from both sides: \( b = 50 - 10 = 40 \).

Answer:

40