This is hardly calculus
y=mx+b
180=m102+b
120=m90+b
subtrract
60=12m solve for m, then b.
y=mx+b
180=m102+b
120=m90+b
subtrract
60=12m solve for m, then b.
Let's define the temperature in degrees Fahrenheit as "x" and the number of chirps per minute as "y". We have two data points: (102, 180) and (90, 120).
To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
First, we need to find the slope:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the two data points:
m = (120 - 180) / (90 - 102)
m = -60 / -12
m = 5
The slope of the line is 5.
Next, we can use the point-slope form of the equation to find the y-intercept:
y - y1 = m(x - x1)
Using the coordinates of one of the data points, let's take (102, 180):
y - 180 = 5(x - 102)
y - 180 = 5x - 510
y = 5x - 330
Therefore, the mathematical model that predicts the number of chirps per minute at a temperature in degrees Fahrenheit is:
chirps per minute = 5*temperature in degrees Fahrenheit - 330
In slope-intercept form, the equation is:
y = 5x - 330
The coefficient of x (5 in this case) represents the rate at which the number of chirps per minute changes with each degree Fahrenheit increase in temperature. The constant term (-330) represents the starting point or the number of chirps at 0 degrees Fahrenheit.