Answer:
C. Function A has a greater rate of change than Function B because 1.25 > 0.3.
Step-by-step explanation:
The rate of change for a linear function can be determined by the slope of the line, which is the coefficient of the x term when the equation is in the form [tex]y = mx + b[/tex], where m is the slope.
For Function A, the rate of change (which is the slope) is given directly by the equation [tex]y = ( \frac{5}{4} )x[/tex]. This means the slope is [tex]( \frac{5}{4} )[/tex] or 1.25. This represents the change in y for each unit change in x.
Function B's rate of change can be calculated using the values in the table by taking the difference in the y-values divided by the difference in the corresponding x-values. For example, using the first two rows of the table (with x-values of 5 and 10, and y-values of 1.5 and 3):
Rate of change for Function B = [tex]( \frac{Change \ in \ y}{Change \ in \ x} ) = ( \frac{3 - 1.5}{10 - 5} ) = ( \frac{1.5}{5} ) = 0.3[/tex]
Comparing the rates of change for Function A and Function B, we see that Function A has a rate of change of 1.25, while Function B has a rate of change of 0.3. Thus, Function A has a greater rate of change than Function B because 1.25 is indeed greater than 0.3.
So the correct statement is:
C. Function A has a greater rate of change than Function B because 1.25 > 0.3.
Hope this helps!
