Find the gradient of the line joining (3, 8) and (6, 12).

The gradient (or slope) of the line joining two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:

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

For the points \((3, 8)\) and \((6, 12)\):

- \(x_1 = 3\), \(y_1 = 8\)
- \(x_2 = 6\), \(y_2 = 12\)

Substituting these values into the formula:

\[ m = \frac{12 - 8}{6 - 3} \]

\[ m = \frac{4}{3} \]

Thus, the gradient of the line joining the points \((3, 8)\) and \((6, 12)\) is \(\frac{4}{3}\).

If you have any questions or want more details, let me know!

Here are some related questions for further exploration:

1. How do you find the midpoint of a line segment given two points?
2. What does it mean when the gradient of a line is zero?
3. How do you determine the gradient of a line from its equation in slope-intercept form?
4. Can the gradient of a line be a negative value? What does that indicate?
5. How does the gradient relate to the angle a line makes with the x-axis?
6. What is the difference between a line with a positive gradient and a line with a negative gradient?
7. How can you use the gradient to find the perpendicular bisector of a line segment?
8. How do you calculate the gradient of a line in three-dimensional space?

**Tip**: Always double-check your calculations when finding the gradient to ensure accuracy, especially with subtraction, as sign errors can lead to incorrect results.

Learn how to find the gradient (or slope) of a line using the points (3, 8) and (6, 12). Step-by-step explanation with calculations provided. Suitable for students in Grades 9-12 studying geometry and analytical geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation