Question

Complete the table and identify the equation for function B.


On observing, we see that function B has slope compared to slope of function A.

• A. smaller
• B. greater
• C. same

Answer 1

The correct option is B greater

Equation for Function A is y = 2x - 3

The above equation is in the form of
y = mx + c

We know in the equation y = mx + c, "m" indicates the slope which is also known as the rate of change of a function.

So, on comparison with the equation, we see:

Slope = rate of change of = 2
Function A

Now for analyzing the table for Function B, we see:

$\text{When x = 1, y =}5\times 1-1=4$

$\text{When x = 2, y =}5\times 2-2=8$

$\text{So, when x = 3, y =}5\times 3-3=12$

Completing the table, we see

x	y
1	4
2	8
3	12

$\text{∴ Rate of change of Function B}=\frac{\text{Change in y}}{\text{Change in x}}$

$=\frac{8-4}{2-1}$

$=4$

∴ Slope = rate of change of = 4
Function B

Therefore, Function B has greater slope than Function A.