Question

Use the pattern of the rate of change to complete the table below that represents a linear function.

Answer 1

1. When x = 2, y = -4

2. When x = 3, y = -7

Step-by-step explanation

Standard form of a linear function

`y\text{ = ax + b}`

Determine the values of a and b

`\begin{gathered} f(-2)\text{ = 8} \\ 8\text{ = a\lparen-2\rparen + b} \\ 8\text{ = -2a + b ................................equ 1} \end{gathered}`
`\begin{gathered} f(-1)\text{ = 5} \\ 5\text{ = -a + b ................................equ 2} \end{gathered}`

Multiply equation 2 by -1

`equ\text{ 2 }*-1\Rightarrow\text{ -5 = a - b ................equ 3}`

Add equation 1 to equation 3

8 = -2a + b

-5 = a - b

---------------

3 = -a + 0

a = -3

Substitute the value of a into equation 1 to determine the value of b

8 = -2(-3) +b

8 = 6 + b

8-6 = b

b = 2

Rewrite the equation

`y\text{ = -3x + 2}`

Now, complete the table using the equation.

When x = 2,

y = -3(2) + 2

y = -6 + 2

y = -4

When x = 3,

y = -3(3) + 2

y = -9 + 2

y = -7