To graph the equation \(\( y = -2x + 2 \)\) on the coordinate plane, follow these step-by-step instructions:
### Step 1: Identify the Slope and Y-Intercept
The given equation is in slope-intercept form, \(\( y = mx + b \)\), where:
- \(\( m \)\) is the slope of the line.
- \(\( b \)\) is the y-intercept of the line.
For the equation \(\( y = -2x + 2 \)\):
- The slope \(\( m \)\) is \(\(-2\)\).
- The y-intercept \(\( b \)\) is \(\( 2 \)\).
### Step 2: Plot the Y-Intercept
The y-intercept is the point where the line crosses the y-axis. This occurs when \(\( x = 0 \)\).
To plot the y-intercept:
- Find the point \(\((0, 2)\)\).
- On the coordinate plane, mark a point at \(\((0, 2)\)\).
### Step 3: Use the Slope to Find Another Point
The slope \(\( m = -2 \)\) indicates that for every 1 unit increase in \(\( x \)\), \(\( y \)\) decreases by 2 units. The slope can be written as \(\(-2/1\)\).
To find another point:
- Start from the y-intercept \(\((0, 2)\)\).
- Move 1 unit to the right (positive direction), which corresponds to increasing \(\( x \)\) by 1.
- From there, move 2 units down (negative direction), which corresponds to decreasing \(\( y \)\) by 2.
This gives you a new point at \(\((1, 0)\)\).
### Step 4: Plot the Second Point
On the coordinate plane, mark the point \(\((1, 0)\)\).
### Step 5: Draw the Line
Using a ruler, draw a straight line passing through the points \(\((0, 2)\)\) and \(\((1, 0)\)\). Extend the line in both directions, and add arrowheads to indicate that the line continues infinitely.
### Step 6: Label the Line
Label the line with its equation \(\( y = -2x + 2 \)\).
### Verification
Optionally, you can check a few more points to ensure the accuracy of the graph. For example:
- If \(\( x = -1 \)\), then \(\( y = -2(-1) + 2 = 4 \)\). Plot the point \(\((-1, 4)\)\).
- If \(\( x = 2 \)\), then \(\( y = -2(2) + 2 = -2 \)\). Plot the point \(\((2, -2)\)\).
Here are the steps summarized in visual terms:
1. Plot the y-intercept \(\((0, 2)\)\).
2. Use the slope to find another point, such as \(\((1, 0)\)\).
3. Draw the line through these points and label it with the equation \(\( y = -2x + 2 \)\).
Following these steps, you'll accurately graph the equation \(\( y = -2x + 2 \)\) on the coordinate plane.
