Graph a line parallel to y=-2/3x+5 with a y intercept of2

To graph a line parallel to the given line \( y = -\frac{2}{3}x + 5 \) with a \( y \)-intercept of 2, we need to follow these steps:

### Step 1: Understand the Properties of Parallel Lines
- **Parallel lines** have the same slope. 
- The slope of the given line \( y = -\frac{2}{3}x + 5 \) is \(-\frac{2}{3}\).

### Step 2: Write the Equation of the New Line
- Since we want a line that is parallel, it will have the same slope: \(-\frac{2}{3}\).
- The general equation for a line is: \( y = mx + b \), where:
  - \( m \) is the slope.
  - \( b \) is the \( y \)-intercept.

- For our new line, the slope \( m = -\frac{2}{3} \) and \( y \)-intercept \( b = 2 \).
- Thus, the equation of the new line is:
  \[
  y = -\frac{2}{3}x + 2
  \]

### Step 3: Graph the Line
- Plot the \( y \)-intercept (0, 2) on the graph.
- Use the slope \(-\frac{2}{3}\):
  - From the point (0, 2), move **down 2 units** and **right 3 units** to find another point.
  - Mark this point and draw a line through both points.

Would you like a visual graph of this line? 

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Here are some related questions:
1. How do you find the slope of a line from its equation?
2. What is the difference between parallel and perpendicular lines?
3. How do you graph lines with positive slopes?
4. How can you find the equation of a line given two points?
5. What happens if two lines have the same slope but different intercepts?

**Tip:** Parallel lines will never intersect, as their slopes are identical.

Graph a line parallel to y=-2/3x+5 with a y intercept of 2.

Learn how to graph a line parallel to y = -2/3x + 5 with a y-intercept of 2. This problem involves understanding linear equations, parallel line properties, and using slope-intercept form. Suitable for students in Grades 8-10.

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