To solve the problem in the image:

Problem Breakdown:

The equation provided is $y = 2x - 4$. We need to verify it by completing the table using this equation.

1. Equation: $y = 2x - 4$

2. Table includes given $x$-values and some missing $y$-values:

   $x$	$y$
   -8	?
   -4	?
   0	4
   4	12
   8	?

Step-by-Step Calculation:

• For $x = -8$: $y = 2(-8) - 4 = -16 - 4 = -20$

• For $x = -4$: $y = 2(-4) - 4 = -8 - 4 = -12$

• $x = 0$ and $y = 4$ is already provided (it satisfies the equation).

• $x = 4$ and $y = 12$ is already provided (it satisfies the equation).

• For $x = 8$: $y = 2(8) - 4 = 16 - 4 = 12$

Completed Table:

This confirms that the equation $y = 2x - 4$ fits the given table values.

Would you like further details or clarification on the calculations?

Related Questions:

1. What does the slope ($m$) in the equation $y = 2x - 4$ represent?
2. How would the table change if the equation were $y = 4x + 2$?
3. How can we verify an equation matches a table of values graphically?
4. What is the significance of the $y$-intercept ($-4$) in the equation $y = 2x - 4$?
5. How does the equation $y = 2x - 4$ differ from $y = 2x + 4$?

Tip:

Always substitute $x$-values into the equation systematically to ensure all table values align with the given rule.