The graph represents a linear relationship, and your task is to complete the table and find the equation that represents this relationship.

Let's analyze the graph step by step:

1. Given Data Points:

   • $x = 10$, $y = ?$ (To be determined)
   • $x = 12$, $y = 4$
   • $x = 16$, $y = 8$
   • $x = 20$, $y = ?$ (To be determined)

2. Finding the pattern: The slope (rate of change of $y$ with respect to $x$) can be determined by looking at the points $(12, 4)$ and $(16, 8)$. The change in $y$ is $8 - 4 = 4$, and the change in $x$ is $16 - 12 = 4$. Therefore, the slope $m$ is: $m = \frac{4}{4} = 1$ This tells us that for every increase of 1 unit in $x$, $y$ increases by 1 unit.

3. Finding the y-intercept: The graph appears to pass through $x = 8$ and $y = 0$, so the y-intercept is $y = 0$ when $x = 8$.

4. Equation of the line: Since the slope is 1 and the line passes through $(8, 0)$, we can write the equation in slope-intercept form: $y = x - 8$

5. Completing the table:

   • For $x = 10$, $y = 10 - 8 = 2$
   • For $x = 20$, $y = 20 - 8 = 12$

Thus, the completed table is:

Equation: $y = x - 8$

Would you like more details or have any other questions?

Here are 5 related questions you might find helpful:

1. How can I verify if my equation is correct for any other points on the line?
2. What happens to the slope and intercept if the graph shifts?
3. How do I find the equation of a line when given two points?
4. Can I write this equation in a different form, such as point-slope form?
5. What is the significance of the slope in real-world applications?

Tip: In linear equations, the slope represents the rate of change between the variables, while the y-intercept shows the starting value when the independent variable is zero.