𝑙: 𝑦 = 2𝑥 − 4
𝑚: 𝑦 = −3𝑥 + 6

You have two linear equations for lines \(l\) and \(m\):

1. \( l: y = 2x - 4 \)
2. \( m: y = -3x + 6 \)

To analyze these lines, we can explore their properties:

### 1. **Slopes:**
   The slope of line \( l \) is \( 2 \), and the slope of line \( m \) is \( -3 \). Since the slopes are different, the lines are not parallel.

### 2. **Intersection:**
   To find the intersection point, set the equations equal to each other:
   \[
   2x - 4 = -3x + 6
   \]
   Solve for \(x\):
   \[
   2x + 3x = 6 + 4 \implies 5x = 10 \implies x = 2
   \]
   Substitute \(x = 2\) into either equation to find \(y\):
   \[
   y = 2(2) - 4 = 4 - 4 = 0
   \]
   So the lines intersect at the point \((2, 0)\).

### 3. **Parallel or Perpendicular:**
   Since the slopes \(2\) and \(-3\) are negative reciprocals of each other (\(2 \times -3 = -6\)), the lines are **not perpendicular**. However, the slopes are not equal, so they are not parallel either.

### 4. **Y-Intercepts:**
   - Line \(l\) has a \(y\)-intercept at \((0, -4)\).
   - Line \(m\) has a \(y\)-intercept at \((0, 6)\).

Would you like more details or any specific clarifications?

### Follow-up Questions:
1. What does it mean when two lines are perpendicular?
2. How do you determine if two lines are parallel?
3. What is the general form of a linear equation, and how does it relate to the slope and intercept?
4. How can you calculate the distance between two intersecting lines?
5. What are some applications of finding the intersection point of two lines?

**Tip:** To find the intersection of two lines quickly, equate their \(y\)-values and solve for \(x\).

Explore the intersection of two linear equations, y = 2x − 4 and y = −3x + 6. This guide covers key algebraic concepts, including slope, y-intercepts, and intersection points. Learn how to determine if lines are parallel or perpendicular. Suitable for Grades 8-10.

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