What is the slope of the line that passes through the points left parenthesis, 4, comma, minus, 6, right parenthesis(4,−6) and left parenthesis, minus, 2, comma, 3, right parenthesis(−2,3)? Write your answer in simplest form.

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

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

Given the points \( (4, -6) \) and \( (-2, 3) \), we can assign:
- \( x_1 = 4 \), \( y_1 = -6 \)
- \( x_2 = -2 \), \( y_2 = 3 \)

Now, substitute these values into the formula:

\[
m = \frac{{3 - (-6)}}{{-2 - 4}} = \frac{{3 + 6}}{{-2 - 4}} = \frac{9}{-6} = -\frac{3}{2}
\]

So, the slope of the line is:

\[
m = -\frac{3}{2}
\]

Would you like more details or have any questions?

Here are five related questions for practice:
1. What is the slope of a line passing through the points \( (2, 5) \) and \( (-3, -4) \)?
2. How do you interpret the slope of \( -\frac{3}{2} \) in the context of this line?
3. If the slope is positive, what does that tell you about the direction of the line?
4. How do you find the y-intercept of a line given its slope and a point?
5. Can two points define more than one unique line? Why or why not?

**Tip**: The slope of a line indicates its steepness and direction—positive slopes go upward, negative slopes go downward.

What is the slope of the line that passes through the points (4, −6) and (−2, 3)? Write your answer in simplest form.

Learn how to calculate the slope of a line passing through the points (4, −6) and (−2, 3). This step-by-step guide explains the slope formula and the process to simplify the result, suitable for Grades 8-10.

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