Question

Which of these function has a greater rate of change than the function graphed bean why

1
3
12
.
12
Oya 2x + 12, because the rate of change of the graphed function is 9
y = 10x + 1, because the rate of change of the graphed function is 3
Oy10x 1, because the rate of change of the graphed function is 9
y = 212, because the rate of change of the graphed function in 3

Answer 1

The 2nd option is correct.

i.e.

y = 10+1, because the rate of change of the graphed function is 3.

Explanation:

From the graph,

Taking two points

• (0, 0)

• (3, 9)

Finding the rate of change or slope between (0, 0) and (3, 9)

Using the formula

Rate of change = Slope = m = [y₂ - y₁] / [x₂ - x₁]

= [9 - 0] / [3 - 0]

= 9 / 1

= 3

Thus, the rate of change or slope of the line = m = 3

The slope-intercept form of the line equation

`y = mx+b`

where

• m is the rate of change or slope

• b is the y-intercept

Considering the function in 2nd option

y = 10x+1

Comparing with the slope-intercept form of the line equation y = mx+b

The rate of change or slope = m = 10

Conclusion:

The rate of change or slope of the graphed line: m = 3

The rate of change or slope of y = 10x+1 is: m = 10

Thus, the rate of change of y = 10x+1 i.e. m = 10 is greater than the rate of change of the graphed line i.e. m = 3.

Hence, the 2nd option is correct.

i.e.

y = 10+1, because the rate of change of the graphed function is 3.