Biologist have found that the number of chirps some crickets make per minute is related to temperature. The relationship is very close to being linear. When crickets chirp 124 times a minutes the temperature is about 68°F. When they chirp 172 times a minutes, it is about 80°F. Find an equation for the line that models this situation.
To find the equation for the line that models the situation, we need to determine the slope and the y-intercept.
Let's use the temperature as the independent variable (x) and the number of chirps per minute as the dependent variable (y). We can use the two given points (68, 124) and (80, 172) to find the equation.
Using the slope formula:
Slope (m) = (change in y) / (change in x)
= (172 - 124) / (80 - 68)
= 48 / 12
= 4
So, the slope (m) is 4.
Using the point-slope form of a linear equation:
y - y1 = m(x - x1), where (x1, y1) is a given point on the line.
Let's use the first given point (68, 124) in the equation:
y - 124 = 4(x - 68)
Expanding the equation:
y - 124 = 4x - 272
Now, let's isolate y by adding 124 to both sides:
y = 4x - 272 + 124
y = 4x - 148
Therefore, the equation for the line that models this situation is:
y = 4x - 148