To complete the ordered pairs [tex]\((0, \ldots)\)[/tex], [tex]\((2, \ldots)\)[/tex], and [tex]\((-1, \ldots)\)[/tex] for the given linear equation [tex]\( y = 2x - 1 \)[/tex], we will find the corresponding [tex]\( y \)[/tex]-values for each [tex]\( x \)[/tex]-value.
### Step-by-Step Solution:
1. Calculate [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = 2x - 1 \)[/tex]:
[tex]\[
y = 2(0) - 1 = -1
\][/tex]
So, the ordered pair is [tex]\((0, -1)\)[/tex].
2. Calculate [tex]\( y \)[/tex] when [tex]\( x = 2 \)[/tex]:
Substitute [tex]\( x = 2 \)[/tex] into the equation [tex]\( y = 2x - 1 \)[/tex]:
[tex]\[
y = 2(2) - 1 = 4 - 1 = 3
\][/tex]
So, the ordered pair is [tex]\((2, 3)\)[/tex].
3. Calculate [tex]\( y \)[/tex] when [tex]\( x = -1 \)[/tex]:
Substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 2x - 1 \)[/tex]:
[tex]\[
y = 2(-1) - 1 = -2 - 1 = -3
\][/tex]
So, the ordered pair is [tex]\((-1, -3)\)[/tex].
### Completed Ordered Pairs:
- [tex]\((0, -1)\)[/tex]
- [tex]\((2, 3)\)[/tex]
- [tex]\((-1, -3)\)[/tex]
### Graphing the Equation:
To graph the equation [tex]\( y = 2x - 1 \)[/tex] using the ordered pairs [tex]\((0, -1)\)[/tex], [tex]\((2, 3)\)[/tex], and [tex]\((-1, -3)\)[/tex], follow these steps:
1. Plot the points [tex]\((0, -1)\)[/tex], [tex]\((2, 3)\)[/tex], and [tex]\((-1, -3)\)[/tex] on the coordinate plane.
2. Draw a straight line passing through these points.
Since [tex]\( y = 2x - 1 \)[/tex] is a linear equation, the graph will be a straight line.
