Question

linear function a and linear function b both have the same input values as shown below. why will the output values for linear function a always be different than the corresponding output values for linear function b?

linear function a
\\(\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline 1 & 3 \\\\\\hline 3 & 7 \\\\\\hline 5 & 11 \\\\\\hline 7 & 15 \\\\\\hline 9 & 19 \\\\\\hline\\end{array}$$

\\)

linear function b
\\(\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline 1 & 4 \\\\\\hline 3 & 8 \\\\\\hline 5 & 12 \\\\\\hline 7 & 16 \\\\\\hline 9 & 20 \\\\\\hline\\end{array}$$

\\)

• the initial values of the two functions are different, and the rates of change of the two functions are also different.
• the initial values of the two functions are different, and the rates of change of the two functions are the same.
• the initial values of the two functions are the same, and the rates of change of the two functions are different.
• the initial values of the two functions are the same, and the rates of change of the two functions are also the same.

Explanation:

Calculate rate of change

Using the Rate of Change knowledge point

$$
LATEXBLOCK0
$$

Determine initial values

Using the Initial Value of Linear Function knowledge point

$$
LATEXBLOCK1
$$

Compare functions

Using the Rate of Change and Initial Value of Linear Function knowledge points

$$
LATEXBLOCK2
$$

Answer:

• The initial values of the two functions are different, and the rates of change of the two functions are also different.
• The initial values of the two functions are different, and the rates of change of the two functions are the same. (Correct answer)
• The initial values of the two functions are the same, and the rates of change of the two functions are different.
• The initial values of the two functions are the same, and the rates of change of the two functions are also the same.