Final answer:
The slope of the function f(x) = 4 + 5x is 5. The slope indicates how much f(x) increases for each increase of 1 in x. For prediction purposes, a regression line like ŷ = -173.51 + 4.83x can be used if the correlation is statistically significant.
Step-by-step explanation:
The slope of a linear function like f(x) = 4 + 5x is the coefficient of x. This is because a linear function has the general form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope m is 5, which means for every increase of 1 in x, f(x) increases by 5. The slope indicates how steep the line is, and it is the same across the entire line.
Looking at Figure A1, it serves as an example of how the slope and y-intercept determine the shape of a line. Here the slope (m) is 3 and the y-intercept (b) is 9. However, these values are specific to Figure A1's line, not to the provided function f(x) = 4 + 5x.
Regarding the least-squares regression line, yes, it can be used for prediction. If the correlation coefficient (r) has a significant value and the hypothesis test does not reject : ρ = 0 at α = 0.05, it indicates a significantly linear relationship between the variables, therefore using ý = -173.51 + 4.83x for prediction is appropriate.