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write the equation of each line in slope intercept form

To write the equation of the line in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we need to:

1. **Identify two points** on the line to calculate the slope (\( m \)).
2. **Determine the y-intercept** \( b \), which is where the line crosses the y-axis.

### From the image:
- The line appears to pass through two points: \( (0, 0) \) and \( (2, 4) \).
  
#### Step 1: Calculate the slope \( m \)
The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (0, 0) \) and \( (2, 4) \):
\[
m = \frac{4 - 0}{2 - 0} = \frac{4}{2} = 2
\]
So, the slope \( m = 2 \).

#### Step 2: Identify the y-intercept \( b \)
Since the line passes through the origin \( (0, 0) \), the y-intercept \( b = 0 \).

#### Final equation of the line:
\[
y = 2x
\]

This is the equation of the line in slope-intercept form.

Would you like more details or have any further questions?

### Relative questions:
1. What is the general process to calculate the slope of a line?
2. How do you find the y-intercept if the line doesn't pass through the origin?
3. How can you derive the equation of a line if given two points?
4. How does the slope affect the angle of the line?
5. What is the equation for a vertical line, and why is its slope undefined?

**Tip:** Always check the coordinates of points used to calculate the slope accurately, as this step is crucial for finding the correct equation.

Learn how to derive the equation of a line in slope-intercept form from two points. This example includes key steps in calculating the slope and determining the y-intercept. Ideal for students in Grades 8-10 studying linear equations.

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