Given below are descriptions of two lines.

Line 1: Goes through (-13,-31) and (3,17)

Line 2: Goes through (12,0) and (0,4)

The slope of Line 1 is m=m=

The slope of Line 2 is m=m=

To find the slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

### **Slope of Line 1:**
The points are \((-13, -31)\) and \((3, 17)\).

\[
m_1 = \frac{17 - (-31)}{3 - (-13)} = \frac{17 + 31}{3 + 13} = \frac{48}{16} = 3
\]

So, the slope of Line 1 is \( m_1 = 3 \).

### **Slope of Line 2:**
The points are \((12, 0)\) and \((0, 4)\).

\[
m_2 = \frac{4 - 0}{0 - 12} = \frac{4}{-12} = -\frac{1}{3}
\]

So, the slope of Line 2 is \( m_2 = -\frac{1}{3} \).

### Final Answer:
- Slope of Line 1: \( m_1 = 3 \)
- Slope of Line 2: \( m_2 = -\frac{1}{3} \)

Would you like more details or have any questions?

Here are 5 related questions for you:
1. What is the equation of Line 1 in slope-intercept form?
2. What is the equation of Line 2 in slope-intercept form?
3. Are Line 1 and Line 2 parallel, perpendicular, or neither?
4. What is the distance between the two points on Line 1?
5. What is the y-intercept of Line 2?

**Tip:** To check if two lines are perpendicular, multiply their slopes. If the product is \(-1\), the lines are perpendicular.

Given below are descriptions of two lines.

Line 1: Goes through (-13,-31) and (3,17)

Line 2: Goes through (12,0) and (0,4)

The slope of Line 1 is m=m=

The slope of Line 2 is m=m=

This problem helps students calculate the slopes of two lines passing through points (-13, -31) and (3, 17) for Line 1, and (12, 0) and (0, 4) for Line 2. The problem introduces the slope formula and discusses the relationship between lines. Suitable for Grades 8-10.

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