To plot the points on the line [tex]\( y = 3x - 2 \)[/tex] that correspond with [tex]\( x = -2 \)[/tex], [tex]\( x = 0 \)[/tex], and [tex]\( x = 2 \)[/tex], follow these steps:
1. Determine the y-value for [tex]\( x = -2 \)[/tex]:
- Substitute [tex]\( x = -2 \)[/tex] into the equation [tex]\( y = 3x - 2 \)[/tex].
- [tex]\( y = 3(-2) - 2 \)[/tex]
- [tex]\( y = -6 - 2 \)[/tex]
- [tex]\( y = -8 \)[/tex]
- So, the point is [tex]\((-2, -8)\)[/tex].
2. Determine the y-value for [tex]\( x = 0 \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = 3x - 2 \)[/tex].
- [tex]\( y = 3(0) - 2 \)[/tex]
- [tex]\( y = 0 - 2 \)[/tex]
- [tex]\( y = -2 \)[/tex]
- So, the point is [tex]\((0, -2)\)[/tex].
3. Determine the y-value for [tex]\( x = 2 \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the equation [tex]\( y = 3x - 2 \)[/tex].
- [tex]\( y = 3(2) - 2 \)[/tex]
- [tex]\( y = 6 - 2 \)[/tex]
- [tex]\( y = 4 \)[/tex]
- So, the point is [tex]\((2, 4)\)[/tex].
Now, you have the three points:
- [tex]\((-2, -8)\)[/tex]
- [tex]\((0, -2)\)[/tex]
- [tex]\((2, 4)\)[/tex]
Plotting the Points:
1. Plot [tex]\((-2, -8)\)[/tex]:
- Find [tex]\(-2\)[/tex] on the x-axis.
- Move down to [tex]\(-8\)[/tex] on the y-axis.
- Place a point at [tex]\((-2, -8)\)[/tex].
2. Plot [tex]\((0, -2)\)[/tex]:
- Find [tex]\(0\)[/tex] on the x-axis.
- Move down to [tex]\(-2\)[/tex] on the y-axis.
- Place a point at [tex]\((0, -2)\)[/tex].
3. Plot [tex]\((2, 4)\)[/tex]:
- Find [tex]\(2\)[/tex] on the x-axis.
- Move up to [tex]\(4\)[/tex] on the y-axis.
- Place a point at [tex]\((2, 4)\)[/tex].
By following these steps, you've successfully plotted the required points on the coordinate plane for the line [tex]\( y = 3x - 2 \)[/tex].
