determine the slope for (10, -2) and (1, 1)

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

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

For the points \((10, -2)\) and \((1, 1)\):

\[
m = \frac{1 - (-2)}{1 - 10}
\]

Simplify:

\[
m = \frac{1 + 2}{1 - 10} = \frac{3}{-9} = -\frac{1}{3}
\]

### Final Answer:
The slope of the line is:

\[
m = -\frac{1}{3}
\]

Would you like a deeper explanation or help plotting this? Here are 5 related questions to expand on this topic:

1. How do you calculate the slope of a vertical line?
2. What is the equation of the line passing through \((10, -2)\) and \((1, 1)\)?
3. Can you explain the geometric meaning of a negative slope?
4. How do you calculate the midpoint of the line segment between these points?
5. How does changing one of the points affect the slope?

**Tip:** When calculating slope, double-check the subtraction order of coordinates; reversing it will change the sign!

Learn how to calculate the slope of the line passing through the points (10, -2) and (1, 1) using the slope formula m = (y2 - y1) / (x2 - x1). Includes a detailed step-by-step solution suitable for Grades 7-9.

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