The equation given is $4x + 2y = 8$. We need to find solutions for this equation in terms of pairs $(x, y)$ and complete the table.

Step-by-Step Solution:

1. Solve for $y$: We can rearrange the equation to solve for $y$ in terms of $x$. $4x + 2y = 8$ Subtract $4x$ from both sides: $2y = 8 - 4x$ Divide by 2: $y = 4 - 2x$

2. Complete the Table:

   Now, use this equation $y = 4 - 2x$ to find values of $y$ for given values of $x$:

   • When $x = 0$: $y = 4 - 2(0) = 4$ So, the point is $(0, 4)$.

   • When $x = 1$: $y = 4 - 2(1) = 2$ So, the point is $(1, 2)$.

   • When $x = 2$: $y = 4 - 2(2) = 0$ So, the point is $(2, 0)$.

Thus, the solution set includes points $(0, 4)$, $(1, 2)$, and $(2, 0)$, which you can plot on the graph.

Final Answer:

The set of solutions is: $\{(0, 4), (1, 2), (2, 0)\}$

Would you like more details on how to plot this or expand further?

Related Questions:

1. What happens to $y$ if $x$ increases beyond 2 in the equation $4x + 2y = 8$?
2. How would you describe the slope of the line represented by this equation?
3. Can you find another point on the line, say for $x = 3$?
4. What are the intercepts of the graph for the given equation?
5. How does changing the coefficients in the equation $4x + 2y = 8$ affect the graph?

Tip:

Always solve for one variable in terms of another when dealing with linear equations. This makes finding pairs of solutions easier!