To solve the problem, we need to find the corresponding [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values in the linear equation [tex]\( y = x + 2 \)[/tex].
1. Substituting [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
y = -2 + 2 = 0
\][/tex]
So, when [tex]\( x = -2 \)[/tex], [tex]\( y = 0 \)[/tex].
2. Substituting [tex]\( x = -1 \)[/tex] into the equation:
[tex]\[
y = -1 + 2 = 1
\][/tex]
So, when [tex]\( x = -1 \)[/tex], [tex]\( y = 1 \)[/tex].
3. Substituting [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = 0 + 2 = 2
\][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( y = 2 \)[/tex].
4. Substituting [tex]\( x = 1 \)[/tex] into the equation:
[tex]\[
y = 1 + 2 = 3
\][/tex]
So, when [tex]\( x = 1 \)[/tex], [tex]\( y = 3 \)[/tex].
5. Substituting [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
y = 2 + 2 = 4
\][/tex]
So, when [tex]\( x = 2 \)[/tex], [tex]\( y = 4 \)[/tex].
Now, we can complete the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 0 \\
\hline
-1 & 1 \\
\hline
0 & 2 \\
\hline
1 & 3 \\
\hline
2 & 4 \\
\hline
\end{array}
\][/tex]
To graph the linear equation [tex]\( y = x + 2 \)[/tex]:
1. Plot the points [tex]\((-2, 0)\)[/tex], [tex]\((-1, 1)\)[/tex], [tex]\( (0, 2)\)[/tex], [tex]\( (1, 3)\)[/tex], and [tex]\( (2, 4)\)[/tex] on the coordinate plane.
2. Draw a straight line through these points since the equation represents a linear function.
As a result, you will see that the points lie on a straight line with a slope of [tex]\(1\)[/tex] and a y-intercept of [tex]\(2\)[/tex].
