https://file.aiquickdraw.com/mathbot/file/1727282709184wwvm4r2k.jpg

Let's find the slope for each part of the question:

### a) Slope Between Two Points

The slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points \((-6, 1)\) and \((4, -4)\), we have:
\[
\text{slope} = \frac{-4 - 1}{4 - (-6)} = \frac{-5}{10} = -\frac{1}{2}
\]

### b) Slope of the Line from Equation

Given the equation \(3x - 2y = 4\), we can rewrite this in slope-intercept form \(y = mx + c\) to find the slope \(m\). Solving for \(y\):
\[
-2y = -3x + 4 \implies y = \frac{3}{2}x - 2
\]
Here, the slope \(m = \frac{3}{2}\).

### c) Slope from the Graph

From the graph, we need to determine the change in \(y\) (rise) and the change in \(x\) (run) between two points on the line. Picking any two points on the line, let's use the points where the line crosses the grid lines for accuracy. Assuming the line crosses at points \((-1, -2)\) and \((2, 3)\):
\[
\text{slope} = \frac{3 - (-2)}{2 - (-1)} = \frac{5}{3}
\]

Here are the answers:
- **a)** The slope is \(-\frac{1}{2}\).
- **b)** The slope is \(\frac{3}{2}\).
- **c)** The slope is \(\frac{5}{3}\).

Do you need more details on any of these calculations or have any other questions?

**Further Questions to Consider:**
1. What is the equation of the line passing through the points \((-6, 1)\) and \((4, -4)\)?
2. How do you determine the y-intercept of a line from its equation?
3. Can you find the x- and y-intercepts from the graph provided in part c)?
4. How would the equation change if the line had a different slope but the same y-intercept as in part b)?
5. What are some real-world applications of finding the slope of a line?

**Tip:** When finding the slope from a graph, always try to pick points where the line crosses grid lines at corners of the squares for greater accuracy.

Find the slope between points (-6, 1) and (4, -4), the slope of the line 3x - 2y = 4, and the slope from the graph.

Learn how to find the slope between points (-6, 1) and (4, -4), determine the slope of the line 3x - 2y = 4, and calculate the slope from a graph. Detailed explanation with slope formulas.

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