Question

The graph represents function 1 and the equation represents function 2:

A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3.
Function 2
y = 3x + 1

How much more is the rate of change of function 2 than the rate of change of function 1? (5 points)

1
2
3
4

Answer 1

• The rate of change of function 1 = 0

• The rate of change of the function 2 = 3

Therefore, the rate of change of function 2 is 3 more than the rate of change of function 1.

Hence, option C is true.

Explanation:

Function 1

A horizontal straight line is drawn joining the ordered pairs (0, 3) and (4, 3).

Given the points

• (0, 3)

• (4, 3)

It means

at x = 0, y = 3

at x = 4, y = 3

Since the y-values are same, it means the points lie on a horizontal.

The rate of change or slope of a horizontal line is zero because it does not rise vertically ( i.e. y₁ - y₂ = 0).

Therefore, the rate of change of function 1 = 0

Function 2

y = 3x+1

comparing with the slope-intercept form

y = mx+b

here m is the rate of change or slope and b is the y-intercept

so the rate of change of the function 2 = m = 3

Conclusion:

• The rate of change of function 1 = 0

• The rate of change of the function 2 = 3

Therefore, the rate of change of function 2 is 3 more than the rate of change of function 1.

Hence, option C is true.