Answer:
A. To find a linear equation that models the temperature T when crickets are chirping at x chirps per minute, we need to use two points that are known. In this case, we are given that a cricket produces 120 chirps per minute at 70 degrees F and 168 chirps per minute at 80 degrees F. We can use these two points to find the slope and y-intercept of the line.
The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1)
In this case, we can substitute the given values to get:
m = (168 - 120) / (80 - 70) = 48/10 = 4.8
The y-intercept of a line can be found using the formula: b = y - mx
We can use the point (70, 120) and the slope that we found to get:
b = 120 - (4.8 * 70) = -264
So the linear equation that models the temperature T when crickets are chirping at x chirps per minute is:
T = 4.8x - 264
B. If the crickets are chirping at 150 chirps per minute, we can substitute this value for x in the equation we found above to estimate the temperature:
T = 4.8x - 264
T = 4.8(150) - 264 = 720 - 264 = 456
So the estimated temperature is 456 degrees F.
C. The y-intercept of the line is -264, it represents the temperature when x (chirps per minutes) is zero. In this case it represents the temperature when the cricket is not chirping which is impossible, so it doesn't have any physical meaning.