https://file.aiquickdraw.com/mathbot/file/1726717088090m2sb6194.jpg

To find the equation of the line in the image, let's analyze it step by step.

### Step 1: Identify Points on the Line
Looking at the graph, two distinct points are clearly marked:

- Point 1: \((-6, -6)\)
- Point 2: \((2, -2)\)

### Step 2: Calculate the Slope (m)
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the points \((-6, -6)\) and \((2, -2)\) into the formula:
\[
m = \frac{-2 - (-6)}{2 - (-6)} = \frac{-2 + 6}{2 + 6} = \frac{4}{8} = 0.5
\]

So, the slope \(m = 0.5\).

### Step 3: Use Point-Slope Form to Find the Equation
The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
Using one of the points, say \((2, -2)\), and the slope \(m = 0.5\):
\[
y - (-2) = 0.5(x - 2)
\]
Simplifying:
\[
y + 2 = 0.5(x - 2)
\]
\[
y + 2 = 0.5x - 1
\]
\[
y = 0.5x - 1 - 2
\]
\[
y = 0.5x - 3
\]

### Final Equation
The equation of the line is:
\[
y = 0.5x - 3
\]

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you find the equation of a line given only the slope and one point?
2. Can you explain how to derive the slope formula in more detail?
3. What is the difference between slope-intercept form and point-slope form of a line?
4. How do you convert a linear equation into standard form?
5. How would the equation change if we used a different point on the line?

**Tip:** Always make sure to double-check the coordinates of the points you're using when calculating the slope. Even small errors in reading the graph can affect the outcome.

Find an equation for the line shown in the graph.

Learn how to find the equation of a line from a graph with points (-6, -6) and (2, -2). This problem demonstrates the use of the slope formula and the point-slope form to derive the equation in slope-intercept form, y = 0.5x - 3. Suitable for students in Grades 8-10.

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