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write equation for slope of the line in slope-intercept form

To write the equation of the line in slope-intercept form, which is given by:

\[
y = mx + b
\]

Where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept, the point where the line crosses the y-axis.

### Step 1: Find the Slope (m)
The slope \(m\) is calculated as the "rise over run," or:

\[
m = \frac{\text{change in } y}{\text{change in } x}
\]

From the graph:
- Two points on the line are approximately \((-8, 2)\) and \((0, -4)\).

Now, calculate the slope:
\[
m = \frac{-4 - 2}{0 - (-8)} = \frac{-6}{8} = -\frac{3}{4}
\]

### Step 2: Find the Y-intercept (b)
From the graph, we can observe that the line crosses the y-axis at \((0, -4)\), so the y-intercept \(b = -4\).

### Final Equation:
Substitute \(m = -\frac{3}{4}\) and \(b = -4\) into the slope-intercept form:

\[
y = -\frac{3}{4}x - 4
\]

This is the equation of the line in slope-intercept form.

Would you like any more details or have any questions?

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Here are 5 related questions for further exploration:
1. How would the equation change if the slope were positive?
2. Can you derive the equation if only two points on the line are known?
3. What happens to the equation if the line passes through the origin?
4. How do you convert the slope-intercept form to standard form?
5. How can you determine the slope if the graph is not given?

**Tip:** Always check the coordinates of the points carefully when calculating slope to avoid errors.

Write the equation for the line in slope-intercept form

Learn how to find the equation of a line in slope-intercept form by identifying the slope and y-intercept from a graph. This problem involves key concepts such as slope and linear equations. Suitable for students in Grades 8-10.

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