Find the slope of the line joining the points left parenthesis 5 comma 1 right parenthesis and left parenthesis 8 comma negative 3 right parenthesis.

To find the slope of the line joining the points \( (5, 1) \) and \( (8, -3) \), we use the slope formula:

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

Where:
- \( (x_1, y_1) = (5, 1) \)
- \( (x_2, y_2) = (8, -3) \)

Now, substitute the coordinates into the formula:

\[
m = \frac{-3 - 1}{8 - 5} = \frac{-4}{3}
\]

So, the slope of the line is:

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

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What does the slope of a line represent geometrically?
2. How would the slope change if the points were reversed?
3. Can you find the equation of the line passing through these points?
4. What is the y-intercept of the line with this slope, given one of the points?
5. How do parallel lines relate in terms of their slopes?

**Tip:** When two points on a line have the same x-coordinate, the line is vertical, and its slope is undefined.

Find the slope of the line joining the points (5, 1) and (8, -3).

Learn how to calculate the slope of a line passing through the points (5, 1) and (8, -3). This step-by-step solution covers key concepts in algebra and coordinate geometry, using the slope formula. Ideal for students in Grades 8-10.

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