Question

Identify the slope and y intercept. Then, graph the linear equation.`y=-\frac{2}{3}x+6`Begin with `m,`the slope:

Answer 1

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

1. **Slope (m)**: The coefficient of \( x \) is the slope. Here, \( m = -\frac{2}{3} \).

2. **Y-intercept (b)**: The constant term is the y-intercept. Here, \( b = 6 \).

So, we have:

- Slope (m): \( -\frac{2}{3} \)
- Y-intercept (b): \( 6 \)

### Graphing the Equation

1. **Plot the Y-intercept**: Start by plotting the point \( (0, 6) \) on the graph.

2. **Use the Slope**: From the y-intercept, use the slope to find another point. The slope \( -\frac{2}{3} \) means that for every 3 units you move to the right (positive x-direction), you move 2 units down (negative y-direction).

- Start at \( (0, 6) \).
- Move right 3 units to \( x = 3 \).
- Move down 2 units to \( y = 4 \).
- This gives the point \( (3, 4) \).

3. **Draw the Line**: Plot the points \( (0, 6) \) and \( (3, 4) \), then draw a straight line through these points to represent the equation \( y = -\frac{2}{3}x + 6 \).

### Summary of Points
- Y-intercept: \( (0, 6) \)
- Another point using slope: \( (3, 4) \)

This is how you can graph the equation, and the line will slope downwards from left to right due to the negative slope.