What is the slope of the line that passes through the points left parenthesis, minus, 2, comma, 6, right parenthesis(−2,6) and left parenthesis, minus, 12, comma, 2, right parenthesis(−12,2)? Write your answer in *simplest form*.

Answer

A

To find the slope of the line passing through the points \((-2, 6)\) and \((-12, 2)\), we can use the slope formula:

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

Here, \((x_1, y_1) = (-2, 6)\) and \((x_2, y_2) = (-12, 2)\).

Substituting the values:

\[
m = \frac{2 - 6}{-12 - (-2)} = \frac{-4}{-12 + 2} = \frac{-4}{-10} = \frac{2}{5}
\]

Thus, the slope of the line is \(\frac{2}{5}\).

**Answer: \(\frac{2}{5}\)**

Would you like a detailed explanation of the steps, or do you have any questions?

Here are five related questions to deepen your understanding:
1. How would you find the slope if one of the points were the origin?
2. What is the significance of a positive slope in terms of the line's direction?
3. How would the formula change if the two points had the same x-coordinate?
4. Can you calculate the slope if the y-coordinates of the points are the same?
5. How would you write the equation of this line in point-slope form?

**Tip:** The slope of a line is a measure of its steepness, with positive slopes rising from left to right and negative slopes falling.

What is the slope of the line that passes through the points (−2,6) and (−12,2)? Write your answer in simplest form.

Learn how to find the slope of the line passing through the points (−2,6) and (−12,2) using the slope formula. This problem helps students understand key algebra concepts, like calculating slope and interpreting linear equations. Ideal for Grades 7-9.

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