Let's complete the table of values and find the points that lie on the line described by the equation [tex]\( y = 3x + 4 \)[/tex].
### Step-by-Step Solution:
1. Calculate [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex]:
[tex]\[
y = 3(-2) + 4 = -6 + 4 = -2
\][/tex]
So, the ordered pair is [tex]\( (-2, -2) \)[/tex].
2. Calculate [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 3(0) + 4 = 0 + 4 = 4
\][/tex]
So, the ordered pair is [tex]\( (0, 4) \)[/tex].
3. Calculate [tex]\( y \)[/tex] when [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 3(2) + 4 = 6 + 4 = 10
\][/tex]
So, the ordered pair is [tex]\( (2, 10) \)[/tex].
Now, let's fill out the table of values with these results:
[tex]\[
\begin{array}{|c|c|c|}
\hline
x & y=3x+4 & (x, y) \\
\hline
-2 & -2 & (-2, -2) \\
\hline
0 & 4 & (0, 4) \\
\hline
2 & 10 & (2, 10) \\
\hline
\end{array}
\][/tex]
So, the completed table is:
[tex]\[
\begin{array}{|c|c|c|}
\hline
x & y=3x+4 & (x, y) \\
\hline
-2 & -2 & (-2, -2) \\
\hline
0 & 4 & (0, 4) \\
\hline
2 & 10 & (2, 10) \\
\hline
\end{array}
\][/tex]
### Graphing the Linear Equation:
To graph the linear equation [tex]\( y = 3x + 4 \)[/tex], you need to plot the points [tex]\((-2, -2)\)[/tex], [tex]\((0, 4)\)[/tex], and [tex]\((2, 10)\)[/tex] on a Cartesian plane. Then, draw a straight line through these points extending in both directions. This line represents the equation [tex]\( y = 3x + 4 \)[/tex].
