ANSWER
1. When x = 2, y = -4
2. When x = 3, y = -7
EXPLANATION
Standard form of a linear function
[tex]y\text{ = ax + b}[/tex]
Determine the values of a and b
[tex]\begin{gathered} f(-2)\text{ = 8} \\ 8\text{ = a\lparen-2\rparen + b} \\ 8\text{ = -2a + b ................................equ 1} \end{gathered}[/tex][tex]\begin{gathered} f(-1)\text{ = 5} \\ 5\text{ = -a + b ................................equ 2} \end{gathered}[/tex]
Multiply equation 2 by -1
[tex]equ\text{ 2 }\times-1\Rightarrow\text{ -5 = a - b ................equ 3}[/tex]
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
[tex]y\text{ = -3x + 2}[/tex]
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
