Graphing Linear Equations - MathsFaculty - Free Printable

Problem Overview:

The task involves completing tables of values for given linear equations and then graphing the lines on a coordinate grid. The equations provided are:

1. \( y = x + 3 \)
2. \( y = 2x + 3 \)
3. \( y = 3x \)
4. \( y = 1 + 2x \)

We will solve each equation step by step, complete the tables, and describe how to graph the lines.

---

Step 1: Solve for \( y \) in each equation

#### Equation 1: \( y = x + 3 \)

- For \( x = 0 \):
\[
y = 0 + 3 = 3
\]
- For \( x = 1 \):
\[
y = 1 + 3 = 4
\]
- For \( x = 2 \):
\[
y = 2 + 3 = 5
\]

Completed Table:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 3 \\
1 & 4 \\
2 & 5 \\
\end{array}
\]

#### Equation 2: \( y = 2x + 3 \)

- For \( x = 0 \):
\[
y = 2(0) + 3 = 3
\]
- For \( x = 1 \):
\[
y = 2(1) + 3 = 5
\]
- For \( x = 2 \):
\[
y = 2(2) + 3 = 7
\]

Completed Table:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 3 \\
1 & 5 \\
2 & 7 \\
\end{array}
\]

#### Equation 3: \( y = 3x \)

- For \( x = 0 \):
\[
y = 3(0) = 0
\]
- For \( x = 1 \):
\[
y = 3(1) = 3
\]
- For \( x = 2 \):
\[
y = 3(2) = 6
\]

Completed Table:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 0 \\
1 & 3 \\
2 & 6 \\
\end{array}
\]

#### Equation 4: \( y = 1 + 2x \)

- For \( x = 0 \):
\[
y = 1 + 2(0) = 1
\]
- For \( x = 1 \):
\[
y = 1 + 2(1) = 3
\]
- For \( x = 2 \):
\[
y = 1 + 2(2) = 5
\]

Completed Table:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 1 \\
1 & 3 \\
2 & 5 \\
\end{array}
\]

---

Step 2: Graph the Lines

Now that we have the tables of values, we can plot the points on the coordinate grid and draw the lines.

#### Graph for Equation 1: \( y = x + 3 \)

- Points: \((0, 3)\), \((1, 4)\), \((2, 5)\)
- Plot these points and draw a straight line through them.

#### Graph for Equation 2: \( y = 2x + 3 \)

- Points: \((0, 3)\), \((1, 5)\), \((2, 7)\)
- Plot these points and draw a straight line through them.

#### Graph for Equation 3: \( y = 3x \)

- Points: \((0, 0)\), \((1, 3)\), \((2, 6)\)
- Plot these points and draw a straight line through them.

#### Graph for Equation 4: \( y = 1 + 2x \)

- Points: \((0, 1)\), \((1, 3)\), \((2, 5)\)
- Plot these points and draw a straight line through them.

---

Final Answer

The completed tables and graphs are as follows:

1. Equation \( y = x + 3 \):
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 3 \\
1 & 4 \\
2 & 5 \\
\end{array}
\]
- Graph: A line passing through \((0, 3)\), \((1, 4)\), and \((2, 5)\).

2. Equation \( y = 2x + 3 \):
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 3 \\
1 & 5 \\
2 & 7 \\
\end{array}
\]
- Graph: A line passing through \((0, 3)\), \((1, 5)\), and \((2, 7)\).

3. Equation \( y = 3x \):
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 0 \\
1 & 3 \\
2 & 6 \\
\end{array}
\]
- Graph: A line passing through \((0, 0)\), \((1, 3)\), and \((2, 6)\).

4. Equation \( y = 1 + 2x \):
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 1 \\
1 & 3 \\
2 & 5 \\
\end{array}
\]
- Graph: A line passing through \((0, 1)\), \((1, 3)\), and \((2, 5)\).

\boxed{\text{Tables and graphs are completed as described above.}}