For each equation, complete the table of values and draw its graph for values of x from -2 to 3. a) y = 2x + 4 b) y = 3x + 2

Here are the completed tables of values for each equation. To draw the graphs, you would plot the coordinate pairs $(x, y)$ from each table and connect them with a straight line.

Question 2: For each equation, complete the table of values and draw its graph for values of $x$ from $-2$ to 3.

• a) $y = 2x + 4$

  Step 1: Substitute each $x$ value into the equation $y = 2x + 4$.
  For $x = -2$, $y = 2(-2) + 4 = -4 + 4 = 0$.
  For $x = -1$, $y = 2(-1) + 4 = -2 + 4 = 2$.
  For $x = 0$, $y = 2(0) + 4 = 0 + 4 = 4$.
  For $x = 1$, $y = 2(1) + 4 = 2 + 4 = 6$.
  For $x = 2$, $y = 2(2) + 4 = 4 + 4 = 8$.
  For $x = 3$, $y = 2(3) + 4 = 6 + 4 = 10$.

  Step 2: Complete the table.

  $$\begin{array}{|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & \textbf{0} & \textbf{2} & \textbf{4} & \textbf{6} & \textbf{8} & \textbf{10} \\ \hline \end{array}$$

  The points to plot are $(-2, 0)$, $(-1, 2)$, $(0, 4)$, $(1, 6)$, $(2, 8)$, $(3, 10)$.

• b) $y = 3x + 2$

  Step 1: Substitute each $x$ value into the equation $y = 3x + 2$.
  For $x = -2$, $y = 3(-2) + 2 = -6 + 2 = -4$.
  For $x = -1$, $y = 3(-1) + 2 = -3 + 2 = -1$.
  For $x = 0$, $y = 3(0) + 2 = 0 + 2 = 2$.
  For $x = 1$, $y = 3(1) + 2 = 3 + 2 = 5$.
  For $x = 2$, $y = 3(2) + 2 = 6 + 2 = 8$.
  For $x = 3$, $y = 3(3) + 2 = 9 + 2 = 11$.

  Step 2: Complete the table.

  $$\begin{array}{|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & \textbf{-4} & \textbf{-1} & \textbf{2} & \textbf{5} & \textbf{8} & \textbf{11} \\ \hline \end{array}$$

  The points to plot are $(-2, -4)$, $(-1, -1)$, $(0, 2)$, $(1, 5)$, $(2, 8)$, $(3, 11)$.

• c) $y = x - 2$

  Step 1: Substitute each $x$ value into the equation $y = x - 2$.
  For $x = -2$, $y = -2 - 2 = -4$.
  For $x = -1$, $y = -1 - 2 = -3$.
  For $x = 0$, $y = 0 - 2 = -2$.
  For $x = 1$, $y = 1 - 2 = -1$.
  For $x = 2$, $y = 2 - 2 = 0$.
  For $x = 3$, $y = 3 - 2 = 1$.

  Step 2: Complete the table.

  $$\begin{array}{|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & \textbf{-4} & \textbf{-3} & \textbf{-2} & \textbf{-1} & \textbf{0} & \textbf{1} \\ \hline \end{array}$$

  The points to plot are $(-2, -4)$, $(-1, -3)$, $(0, -2)$, $(1, -1)$, $(2, 0)$, $(3, 1)$.

• d) $y = 2x - 2$

  Step 1: Substitute each $x$ value into the equation $y = 2x - 2$.
  For $x = -2$, $y = 2(-2) - 2 = -4 - 2 = -6$.
  For $x = -1$, $y = 2(-1) - 2 = -2 - 2 = -4$.
  For $x = 0$, $y = 2(0) - 2 = 0 - 2 = -2$.
  For $x = 1$, $y = 2(1) - 2 = 2 - 2 = 0$.
  For $x = 2$, $y = 2(2) - 2 = 4 - 2 = 2$.
  For $x = 3$, $y = 2(3) - 2 = 6 - 2 = 4$.

  Step 2: Complete the table.

  $$\begin{array}{|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & \textbf{-6} & \textbf{-4} & \textbf{-2} & \textbf{0} & \textbf{2} & \textbf{4} \\ \hline \end{array}$$

  The points to plot are $(-2, -6)$, $(-1, -4)$, $(0, -2)$, $(1, 0)$, $(2, 2)$, $(3, 4)$.

• e) $y = 4 - x$

  Step 1: Substitute each $x$ value into the equation $y = 4 - x$.
  For $x = -2$, $y = 4 - (-2) = 4 + 2 = 6$.
  For $x = -1$, $y = 4 - (-1) = 4 + 1 = 5$.
  For $x = 0$, $y = 4 - 0 = 4$.
  For $x = 1$, $y = 4 - 1 = 3$.
  For $x = 2$, $y = 4 - 2 = 2$.
  For $x = 3$, $y = 4 - 3 = 1$.

  Step 2: Complete the table.

  $$\begin{array}{|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & 6 & 5 & 4 & 3 & 2 & 1 \\ \hline \end{array}$$