Find the slope of the​ line, if it is defined.
Through ​(- 3​,- 12​)
and ​(- 4​,7​)

To find the slope of a line passing through two points \((-3, -12)\) and \((-4, 7)\), we use the slope formula:

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

Where:
- \((x_1, y_1)\) is \((-3, -12)\)
- \((x_2, y_2)\) is \((-4, 7)\)

Now substitute the values into the formula:

\[
m = \frac{7 - (-12)}{-4 - (-3)} = \frac{7 + 12}{-4 + 3} = \frac{19}{-1} = -19
\]

So, the slope of the line is \(m = -19\).

Would you like any further details or clarifications? 

Here are 5 related questions:
1. How would you find the equation of the line using this slope?
2. What is the significance of a negative slope?
3. How can you verify the slope using a graph?
4. What does it mean if the slope is undefined?
5. How would the slope change if the coordinates were swapped?

**Tip**: Always check the order of subtraction when calculating slope to avoid sign errors!

Find the slope of the line, if it is defined. Through (-3, -12) and (-4, 7)

Discover how to calculate the slope of a line passing through the points (-3, -12) and (-4, 7) using the slope formula. This step-by-step solution explains the key algebraic concepts involved, perfect for students in Grades 8-10.

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