To solve the equation [tex]\( x - y = -7 \)[/tex] for the given values of [tex]\( x \)[/tex] and complete the table, follow these steps:
1. Identify the given equation:
[tex]\[ x - y = -7 \][/tex]
2. Rearrange the equation to solve for [tex]\( y \)[/tex]:
[tex]\[ y = x + 7 \][/tex]
Now, let's find the value of [tex]\( y \)[/tex] for [tex]\( x = 2 \)[/tex]:
1. Substitute [tex]\( x = 2 \)[/tex] into the equation [tex]\( y = x + 7 \)[/tex]:
[tex]\[ y = 2 + 7 \][/tex]
2. Perform the addition:
[tex]\[ y = 9 \][/tex]
Now we can complete the table with the calculated value of [tex]\( y \)[/tex].
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
0 & 7 \\
\hline
-7 & 0 \\
\hline
2 & 9 \\
\hline
\end{tabular}
\][/tex]
To graph the equation [tex]\( x - y = -7 \)[/tex]:
1. Plot the points [tex]\((x, y)\)[/tex] from the table: [tex]\((0, 7)\)[/tex], [tex]\((-7, 0)\)[/tex], and [tex]\((2, 9)\)[/tex].
2. Draw a straight line through these points to represent the equation.
The equation of a line in slope-intercept form is [tex]\( y = x + 7 \)[/tex], which indicates a line with slope [tex]\( 1 \)[/tex] and y-intercept [tex]\( 7 \)[/tex].
