Write an equation for the line of best fit that solves for P.
Use the data values to find your line of best fit:
t values: 14, 13, 9, 0
p values: 7, 29, 52, 100
To find the line of best fit, we can use the equation of a line, y = mx + b, where y represents the dependent variable (in this case, p), x represents the independent variable (in this case, t), m represents the slope of the line, and b represents the y-intercept.
To find the slope, m, we can use the formula:
m = (Σ(xy) - n*mean(x)*mean(y)) / (Σ(x^2) - n*(mean(x))^2)
where Σ represents the sum of, n represents the number of data points, xy represents the product of each x and y value, and x^2 represents the square of each x value.
Calculating these values, we get:
Σ(xy) = (14 * 7) + (13 * 29) + (9 * 52) + (0 * 100) = 998
Σ(x^2) = 14^2 + 13^2 + 9^2 + 0^2 = 346
mean(x) = (14 + 13 + 9 + 0) / 4 = 9
mean(y) = (7 + 29 + 52 + 100) / 4 = 47
Substituting these values into the slope formula:
m = (998 - 4 * 9 * 47) / (346 - 4 * 9^2)
m = (-770) / (346 - 324)
m = -770 / 22
m ≈ -35
Now, let's find the y-intercept, b, using the formula:
b = mean(y) - m * mean(x)
b = 47 - (-35) * 9
b = 47 + 315
b = 362
Therefore, the equation for the line of best fit is:
P = -35t + 362