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You need to graph the equation \( y = \frac{2}{3}x - 1 \).

### Step-by-Step Graphing Instructions:

1. **Identify the slope and y-intercept**:
   - The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   - Here, the slope \( m = \frac{2}{3} \) and the y-intercept \( b = -1 \).

2. **Plot the y-intercept**:
   - The y-intercept is \( -1 \), so plot the point \( (0, -1) \) on the y-axis.

3. **Use the slope to find another point**:
   - The slope \( \frac{2}{3} \) means that for every increase of 3 units in the x-direction, the value of y increases by 2 units.
   - Starting from \( (0, -1) \), move 3 units to the right (to \( x = 3 \)) and then 2 units up. This gives the point \( (3, 1) \).
   
4. **Plot the second point**:
   - Plot the point \( (3, 1) \) on the graph.

5. **Draw the line**:
   - Draw a straight line passing through the two points \( (0, -1) \) and \( (3, 1) \). This is the graph of the equation.

Would you like more details on any specific step? Here are five related questions you might find helpful:

1. What is the general form of a linear equation and how does it differ from slope-intercept form?
2. How do you interpret the slope of a line geometrically?
3. How can we determine if two lines are parallel based on their slopes?
4. What does the y-intercept tell us about the graph?
5. How would the graph change if the slope or y-intercept were negative?

**Tip**: When graphing, always start by plotting the y-intercept, then use the slope to determine the direction and steepness of the line.

Graph the linear equation y = 2/3x - 1 by plotting the y-intercept at -1 and using the slope 2/3 to find another point on the line. This problem involves understanding linear equations and slope-intercept form, ideal for students in Grades 7-9.

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