sketch the graph of linear equation y=-2/3x+5

To sketch the graph of the linear equation \( y = -\frac{2}{3}x + 5 \), follow these steps:

1. **Identify the slope and y-intercept**:
   - The slope (\(m\)) is \(-\frac{2}{3}\).
   - The y-intercept (\(b\)) is 5.

2. **Plot the y-intercept**:
   - Start at the point \((0, 5)\) on the y-axis.

3. **Use the slope to find another point**:
   - The slope \(-\frac{2}{3}\) means that 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).
   - From the y-intercept \((0, 5)\), move 3 units to the right to \(x = 3\), and 2 units down to \(y = 3\). This gives you the point \((3, 3)\).

4. **Plot this second point**:
   - Plot the point \((3, 3)\) on the graph.

5. **Draw the line**:
   - Draw a straight line through the points \((0, 5)\) and \((3, 3)\).

Here's a sketch of the graph based on these steps:

![Graph of y = -2/3x + 5](attachment://mnt/data/graph.png)

This is how you graph the linear equation \( y = -\frac{2}{3}x + 5 \).

Would you like more details or have any questions?

### Questions to Expand Understanding:
1. How do you determine the slope from the equation of a line?
2. What is the significance of the y-intercept in a linear equation?
3. How can you graph a line if the equation is in a different form, such as \(Ax + By = C\)?
4. What happens to the graph if the slope is positive instead of negative?
5. How do you find the x-intercept of the equation \( y = -\frac{2}{3}x + 5 \)?
6. How does changing the y-intercept affect the graph of the line?
7. How can you verify that a point lies on the line represented by the equation \( y = -\frac{2}{3}x + 5 \)?
8. How would the graph change if the slope was \(-1\) instead of \(-\frac{2}{3}\)?

### Tip:
When plotting points based on the slope, remember that the direction matters: moving right and up/down corresponds to positive and negative slopes, respectively.

Learn how to sketch the graph of the linear equation y = -2/3x + 5 step-by-step. Understand the slope and y-intercept concepts with practical examples. Suitable for students in Grades 7-9.

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