how to find the slope of (0,-10),(6,-9),(12,-8)

To find the slope of a line that passes through multiple points, you can use the slope formula for any two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Since you're given three points \((0, -10)\), \((6, -9)\), and \((12, -8)\), let's first calculate the slope between two pairs of points to check if they all lie on the same line:

1. **Between \((0, -10)\) and \((6, -9)\)**:
   \[
   m = \frac{-9 - (-10)}{6 - 0} = \frac{-9 + 10}{6} = \frac{1}{6}
   \]

2. **Between \((6, -9)\) and \((12, -8)\)**:
   \[
   m = \frac{-8 - (-9)}{12 - 6} = \frac{-8 + 9}{6} = \frac{1}{6}
   \]

Both calculations give the same slope, \( \frac{1}{6} \). Therefore, the slope of the line that passes through these three points is \( \frac{1}{6} \).

Would you like more details or have any questions about this?

### Relative Questions:
1. How do you determine if points are collinear using the slope?
2. What is the general equation of a line given its slope and a point?
3. How would you find the slope of a vertical line?
4. What is the meaning of a slope of zero?
5. How can you find the y-intercept if you know the slope and one point?

### Tip:
Always check the slope between different pairs of points to ensure they all lie on the same line. If the slopes differ, the points are not collinear.

Learn how to find the slope of points (0,-10), (6,-9), and (12,-8) using the slope formula. This detailed explanation includes step-by-step calculations to determine if the points are collinear. Perfect for students in Grades 8-10 studying linear equations and coordinate 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