To complete the ordered pairs so that each is a solution of the given linear equation [tex]\( y = -2x + 5 \)[/tex], we need to substitute the given [tex]\( x \)[/tex]-value into the equation and solve for [tex]\( y \)[/tex].
Given:
[tex]\[ y = -2x + 5 \][/tex]
Let's calculate [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]:
1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -2(0) + 5 \][/tex]
2. Simplify the expression:
[tex]\[ y = 0 + 5 \][/tex]
[tex]\[ y = 5 \][/tex]
So, the completed ordered pair when [tex]\( x = 0 \)[/tex] is [tex]\( (0, 5) \)[/tex].
The table will look like this:
\begin{tabular}{|c|c|}
\hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline [tex]$0$[/tex] & [tex]$5$[/tex] \\
\hline
\end{tabular}
Next, let's graph the equation [tex]\( y = -2x + 5 \)[/tex].
### Steps to Graph the Equation:
1. Plot the ordered pairs: Start by plotting the point [tex]\((0, 5)\)[/tex] on the graph.
2. Find additional points: To make drawing the line easier, let's calculate a few more points. You can choose any [tex]\( x \)[/tex]-values and calculate the corresponding [tex]\( y \)[/tex]-values.
For example:
- Let [tex]\( x = 1 \)[/tex]:
[tex]\[ y = -2(1) + 5 \][/tex]
[tex]\[ y = -2 + 5 \][/tex]
[tex]\[ y = 3 \][/tex]
So, the point is [tex]\((1, 3)\)[/tex].
- Let [tex]\( x = -1 \)[/tex]:
[tex]\[ y = -2(-1) + 5 \][/tex]
[tex]\[ y = 2 + 5 \][/tex]
[tex]\[ y = 7 \][/tex]
So, the point is [tex]\((-1, 7)\)[/tex].
- Let [tex]\( x = 2 \)[/tex]:
[tex]\[ y = -2(2) + 5 \][/tex]
[tex]\[ y = -4 + 5 \][/tex]
[tex]\[ y = 1 \][/tex]
So, the point is [tex]\((2, 1)\)[/tex].
3. Plot these points: Plot the points [tex]\((1, 3)\)[/tex], [tex]\((-1, 7)\)[/tex], and [tex]\((2, 1)\)[/tex] on the graph.
4. Draw the line: Connect these points with a straight line. The line represents all the solutions to the equation [tex]\( y = -2x + 5 \)[/tex].
Remember, all points on this line satisfy the equation [tex]\( y = -2x + 5 \)[/tex]. By plotting and connecting these points, you've successfully graphed the linear equation.
