Find the slope of the line containing the pair of points.
​(−6​,3​) and ​(4​,5​)

To find the slope of a line passing through two points, we use the slope formula:

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

Given the points \((-6, 3)\) and \((4, 5)\):

- \(x_1 = -6\), \(y_1 = 3\)
- \(x_2 = 4\), \(y_2 = 5\)

Now substitute these values into the formula:

\[
m = \frac{{5 - 3}}{{4 - (-6)}} = \frac{{2}}{{4 + 6}} = \frac{2}{10} = \frac{1}{5}
\]

So, the slope of the line is \(m = \frac{1}{5}\).

Would you like a detailed explanation on slope calculation or have any questions?

Here are 5 related questions for further exploration:
1. How do you interpret the meaning of a positive slope?
2. What is the equation of the line passing through these two points?
3. Can the slope formula be applied to vertical lines? Why or why not?
4. How does the slope change if you swap the two points?
5. What does a slope of \(0\) indicate about the line?

**Tip:** When calculating slope, remember that the order of the points doesn't matter—as long as you're consistent with \(x_1, y_1\) and \(x_2, y_2\).

Find the slope of the line containing the pair of points (−6, 3) and (4, 5).

Learn how to find the slope of a line passing through the points (−6, 3) and (4, 5) using the slope formula. This algebraic problem helps students understand the key concept of slope and how to apply it to points on a coordinate plane. Suitable for students in Grades 7-9.

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