Two functions, P and Q, are described as follows:
Function P
y = 5x + 3
Function Q
The rate of change is 2 and the y-intercept is 4.
How much more is the rate of change of function P than the slope of function Q? (5 points)
3
5
7
8
The rate of change of function P is the coefficient of x, which is 5.
The slope of function Q is 2.
To find the difference between the rate of change of function P and the slope of function Q, we subtract the slope of function Q from the rate of change of function P:
5 - 2 = 3
Therefore, the rate of change of function P is 3 more than the slope of function Q.
The answer is 3.
Jack and Kane buy an equal number of comic books every month. The following equation shows the number of comic books, y, that Jack has after x months:
y = 2x + 15
The following graph shows the number of comic books, y, that Kane has after x months:
Graph shows Months on x axis and Number of Comic Books on y axis. The scale on x axis is shown from 0 to 5 at increments of 1. The scale on y axis is shown from 0 to 21 at increments of 3. The title of the graph is Kanes Comic Books. A straight line is shown which joins the ordered pair 0, 9 and 4, 21
After 2 months, how many more comic books does Jack have than Kane? (5 points)
1
2
4
7
To find out how many more comic books Jack has than Kane after 2 months, we need to substitute x = 2 into both equations and then subtract the resulting values of y.
For Jack (using the equation y = 2x + 15):
y = 2(2) + 15
y = 4 + 15
y = 19
For Kane (using the graph):
After 2 months, Kane has 21 comic books (from the point (2, 21) on the graph).
To find the difference, we subtract the number of comic books Kane has from the number Jack has:
19 - 21 = -2
Therefore, Jack has 2 fewer comic books than Kane after 2 months.
The answer is 2.