Question

identify the slope of intercept. Then, graph the linear equation.
y = -2/3x + 6
begin with B, the y-intercept : ________
move with m, the slope: ________

Answer 1

To identify the slope and intercept of the given linear equation \( y = -\frac{2}{3}x + 6 \):

1. **Identify the y-intercept (B)**:
- The y-intercept is the point where the line crosses the y-axis. In the equation, it is the constant term, which is \( 6 \). So, B = \( 6 \).

2. **Identify the slope (m)**:
- The coefficient of \( x \) represents the slope of the line. In this case, the slope \( m = -\frac{2}{3} \).

With this information, we can summarize:

- Begin with B, the y-intercept: **6**
- Move with m, the slope: **-2/3**

### To graph the linear equation:

1. **Plot the y-intercept**:
- Start at the point \( (0, 6) \) on the graph.

2. **Use the slope to find another point**:
- The slope is \( -\frac{2}{3} \), which means for every 3 units you move to the right (positive direction on the x-axis), you move 2 units down (negative direction on the y-axis).
- Starting from \( (0, 6) \):
- Move right 3 units to \( x = 3 \): From \( (0, 6) \) to \( (3, 6) \).
- Move down 2 units to \( y = 4 \): From \( (3, 6) \) to \( (3, 4) \).
- This gives you the point \( (3, 4) \).

3. **Draw the line**:
- Using the two points \( (0, 6) \) and \( (3, 4) \), draw a straight line extending in both directions.

This is how you would identify the slope and intercept, as well as how to graph the linear equation.