https://file.aiquickdraw.com/mathbot/file/17304091276422wul9why.jpg

To find the slope of the line passing through the points \((-6, 8)\) and \( (4, 12) \), we can use the slope formula:

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

Given:
- Point 1: \( (x_1, y_1) = (-6, 8) \)
- Point 2: \( (x_2, y_2) = (4, 12) \)

Let's substitute these values into the formula:

\[
m = \frac{12 - 8}{4 - (-6)}
\]

Simplifying the numerator and denominator:

\[
m = \frac{4}{4 + 6} = \frac{4}{10} = \frac{2}{5}
\]

So, the slope of the line through the points \((-6, 8)\) and \( (4, 12) \) is:

\[
\boxed{\frac{2}{5}}
\]

Would you like more details or have any other questions?

---

Here are some related questions for further exploration:

1. What is the equation of the line passing through these two points?
2. How would you find the slope if one of the points was changed to \((4, 16)\)?
3. What does a positive slope indicate about the direction of a line?
4. How would the slope change if the points were reversed?
5. How can you find the y-intercept using the slope and one of the points?

**Tip:** The slope of a line shows how steep it is. A positive slope means the line rises from left to right, while a negative slope means it falls.

What is the slope of the line through the points (-6, 8) and (4, 12)?

Learn how to find the slope of a line passing through the points (-6, 8) and (4, 12) using the slope formula. This example provides a step-by-step solution for calculating the slope, a fundamental concept in coordinate geometry. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation