Line e passes through points (7, 8) and (1, 1). Line f passes through points (1, 2) and (7, 9). Are line e and line f parallel or perpendicular?



To determine if two lines are **parallel** or **perpendicular**, we need to calculate their slopes and compare them.

### Step 1: Calculate the slope of line \(e\)
Line \(e\) passes through the points \((7, 8)\) and \((1, 1)\). The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

For line \(e\):
\[
m_e = \frac{1 - 8}{1 - 7} = \frac{-7}{-6} = \frac{7}{6}
\]

### Step 2: Calculate the slope of line \(f\)
Line \(f\) passes through the points \((1, 2)\) and \((7, 9)\). Using the same formula:
\[
m_f = \frac{9 - 2}{7 - 1} = \frac{7}{6}
\]

### Step 3: Compare the slopes
- **Parallel lines** have the same slope. Since \(m_e = m_f = \frac{7}{6}\), lines \(e\) and \(f\) are **parallel**.
- **Perpendicular lines** would have slopes that are negative reciprocals of each other, but that is not the case here.

Thus, **lines \(e\) and \(f\) are parallel**.

Would you like more details or have any questions about this process? Here are some related questions you might find interesting:

1. How can you determine if two lines are perpendicular?
2. What happens when two lines have equal slopes but different intercepts?
3. Can two non-parallel lines with the same slope exist?
4. What is the equation of a line given a point and slope?
5. How do you find the point of intersection of two lines?

**Tip:** When lines have the same slope, they never intersect unless they are the same line!

Line e passes through points (7, 8) and (1, 1). Line f passes through points (1, 2) and (7, 9). Are line e and line f parallel or perpendicular?

Learn how to determine if two lines are parallel or perpendicular by calculating their slopes. This example involves lines passing through points (7, 8), (1, 1) and (1, 2), (7, 9). Suitable for students in Grades 8-10, this problem covers key concepts in coordinate geometry and slope comparisons.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation