To plot the linear relationship [tex]\( y = 2x - 1 \)[/tex] on the Cartesian plane, we can start by creating a table of values. We will select some values of [tex]\( x \)[/tex], compute the corresponding [tex]\( y \)[/tex] values using the equation, and then use these points to draw the line.
Here are the steps:
1. Create a Table of Values:
Let's choose the following values for [tex]\( x \)[/tex]: [tex]\(-2\)[/tex], [tex]\(-1\)[/tex], [tex]\(0\)[/tex], [tex]\(1\)[/tex], and [tex]\(2\)[/tex].
| [tex]\( x \)[/tex] | [tex]\( -2 \)[/tex] | [tex]\( -1 \)[/tex] | [tex]\( 0 \)[/tex] | [tex]\( 1 \)[/tex] | [tex]\( 2 \)[/tex] |
|---------|:--------:|:--------:|:-------:|:-------:|:-------:|
| [tex]\( y \)[/tex] | | | | | |
2. Compute the Corresponding [tex]\( y \)[/tex] Values:
Using the equation [tex]\( y = 2x - 1 \)[/tex]:
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = 2(-2) - 1 = -4 - 1 = -5
\][/tex]
- For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = 2(-1) - 1 = -2 - 1 = -3
\][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 2(0) - 1 = 0 - 1 = -1
\][/tex]
- For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 2(1) - 1 = 2 - 1 = 1
\][/tex]
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 2(2) - 1 = 4 - 1 = 3
\][/tex]
Now we can complete our table:
| [tex]\( x \)[/tex] | [tex]\( -2 \)[/tex] | [tex]\( -1 \)[/tex] | [tex]\( 0 \)[/tex] | [tex]\( 1 \)[/tex] | [tex]\( 2 \)[/tex] |
|---------|:--------:|:--------:|:-------:|:-------:|:-------:|
| [tex]\( y \)[/tex] | -5 | -3 | -1 | 1 | 3 |
3. Plot the Points:
Plot each pair [tex]\((x, y)\)[/tex] from the table above on the Cartesian plane:
- [tex]\(( -2, -5 )\)[/tex]
- [tex]\(( -1, -3 )\)[/tex]
- [tex]\(( 0, -1 )\)[/tex]
- [tex]\(( 1, 1 )\)[/tex]
- [tex]\(( 2, 3 )\)[/tex]
4. Draw the Line:
Once you have plotted these points, draw a straight line through them. This line represents the linear relationship [tex]\( y = 2x - 1 \)[/tex].
By following these steps, you will successfully plot the linear equation [tex]\( y = 2x - 1 \)[/tex] on the Cartesian plane.
