Question

The given table and graph represents two functions.

Function 1:

Time in years (x)	Height in ft (y)
1	20
2	35
3	50

Function 2:


Which of the following has a greater rate of change and write its equation?

• A. Function 2 has greater rate of change, y = 18x - 3
• B. Function 1 has greater rate of change, y = 18x - 3
• C. Function 1 has greater rate of change, y = 18x + 3
• D. Function 2 has greater rate of change, y = 18x + 3

Answer 1

The correct option is D Function 2 has greater rate of change, y = 18x + 3

Let us consider function 1:

Time in years (x)	Height in ft (y)
1	20
2	35
3	50

So,
When x = 1, y = 20

When x = 2 , y = 35

When x = 3, y = 50

$\text{Rate of change of a function}=\frac{\text{Change in y}}{\text{Change in x}}$

Let us consider any two points, say
(1, 20) and (2, 35)

$\text{∴ Rate of change for functon 1 =}\frac{35-20}{2-1}$

$=15$


Let us consider function 2:


$\text{Rate of change of a function}=\frac{\text{Change in y}}{\text{Change in x}}$

Let us consider the two points on the graph, say (0.5, 12) and (1, 21)

$\text{∴ Rate of change for functon 2 =}\frac{21-12}{1-0.5}$

$=\frac{9}{0.5}$

$=18$

Therefore, function 2 have greater rate of change.

Let the y-intercept of function 2 be 'd'

So, equation for function 2 is
y = 18x + d

Substituting the point (1, 21) from the graph in the equation, we get:

$21=18\times 1+d$

$\Rightarrow 21=18+d$

$\Rightarrow d=3$

∴ Value of y-intercept for function 2 = 3

So, equation for function 2 is
y = 18x + 3