Draw a coordinate plane and graph the line `y=2x-4`. Identify the slope and the y - intercept.

Answer

To solve the problem of graphing the line \( y = 2x - 4 \) on a coordinate plane and identifying the slope and y-intercept, follow these steps:

### Step-by-Step Solution:

1. **Draw the Coordinate Plane**:
- Begin by drawing a horizontal line for the x-axis and a vertical line for the y-axis. Label the axes. Mark points on both axes, including positive and negative values.

2. **Identify the Equation**:
- The equation given is \( y = 2x - 4 \). This is in the slope-intercept form \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept.

3. **Identify the Slope and Y-Intercept**:
- From the equation \( y = 2x - 4 \):
- The slope \( m \) is \( 2 \).
- The y-intercept \( c \) is \( -4 \).

4. **Create a Table of Values**:
- Choose several values for \( x \) to find corresponding \( y \) values:
- If \( x = 0 \), then \( y = 2(0) - 4 = -4 \) → Point (0, -4)
- If \( x = 2 \), then \( y = 2(2) - 4 = 0 \) → Point (2, 0)
- If \( x = 3 \), then \( y = 2(3) - 4 = 2 \) → Point (3, 2)
- If \( x = -1 \), then \( y = 2(-1) - 4 = -6 \) → Point (-1, -6)

5. **Plot the Points**:
- On the coordinate plane, plot the points obtained from the table:
- (0, -4)
- (2, 0)
- (3, 2)
- (-1, -6)

6. **Draw the Line**:
- Connect the plotted points with a straight line, extending the line in both directions. This line represents the equation \( y = 2x - 4 \).

7. **Final Identification**:
- Confirm the slope and y-intercept:
- Slope \( m = 2 \)
- Y-intercept \( c = -4 \)

### Summary of Results:
- The slope of the line is \( 2 \).
- The y-intercept of the line is \( -4 \).