Sure, to graph the line given by the equation [tex]\( y = -2x + 2 \)[/tex], let's go through the steps:
### Step 1: Identify the slope and y-intercept
The equation of the line is in the slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
For the equation [tex]\( y = -2x + 2 \)[/tex]:
- Slope (m): -2
- Y-intercept (b): 2
### Step 2: Plot the y-intercept
The y-intercept is the point where the line crosses the y-axis. For [tex]\( y = -2x + 2 \)[/tex], the y-intercept is at [tex]\( y = 2 \)[/tex]. So, plot the point (0, 2) on the graph.
### Step 3: Use the slope to find another point
The slope [tex]\( m \)[/tex] tells us how to move from the y-intercept to another point on the line. A slope of -2 means that for every 1 unit you move to the right (positive direction along the x-axis), you move 2 units down (negative direction along the y-axis).
Starting from the point (0, 2):
- Move 1 unit to the right: [tex]\( x = 0 + 1 = 1 \)[/tex]
- Move 2 units down: [tex]\( y = 2 - 2 = 0 \)[/tex]
So, another point on the line is (1, 0).
### Step 4: Plot the second point
Plot the point (1, 0) on the graph.
### Step 5: Draw the line
Use a straightedge to draw a line through the points (0, 2) and (1, 0). Extend the line in both directions, and add arrows at the ends to indicate that the line goes on infinitely.
### Step 6: Label the line
Label the line with its equation [tex]\( y = -2x + 2 \)[/tex].
### Example Graph
Here's how the graph should look like:
1. The y-intercept at (0,2).
2. Another point at (1,0).
3. The straight line passing through these points, extending infinitely in both directions.
```plaintext
y
↑
4|
3|
2|------(0,2)-------
1|
0|----- (1,0) ----+
-1|
-2|
-3|
-4|
-10 -5 0 5 10
x
```
By following these steps, you can successfully graph the line [tex]\( y = -2x + 2 \)[/tex].
