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What is the equation of the line modeled in the graph?

The red line in the graph appears to be a straight line, meaning it represents a linear equation. To find the equation of the line, we need two key pieces of information:

1. **Slope (m)**: The slope is the ratio of the vertical change ("rise") to the horizontal change ("run").
2. **Y-intercept (b)**: The y-intercept is the point where the line crosses the y-axis.

### Step 1: Identify two points on the line
From the image, two points that the line clearly passes through are:
- Point 1: \( (2, -4) \)
- Point 2: \( (4, 2) \)

### Step 2: Calculate the slope (m)
The slope \( m \) is given by:

\[
m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{2 - (-4)}}{{4 - 2}} = \frac{{6}}{{2}} = 3
\]

So, the slope \( m = 3 \).

### Step 3: Use the slope-intercept form
The slope-intercept form of a line is:

\[
y = mx + b
\]

We know \( m = 3 \), so we substitute one of the points into the equation to solve for \( b \). Using the point \( (2, -4) \):

\[
-4 = 3(2) + b
\]
\[
-4 = 6 + b
\]
\[
b = -4 - 6 = -10
\]

### Final equation of the line:
\[
y = 3x - 10
\]

This is the equation of the red line in the graph.

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Would you like further clarification or details on any step? Here are 5 related questions to explore further:

1. What is the significance of the slope and y-intercept in linear equations?
2. How would the graph change if the slope was negative?
3. What is the general process for converting between slope-intercept form and standard form?
4. Can you determine the x-intercept of the line from the equation?
5. How can you graph a line if you're given the equation directly?

**Tip:** When graphing lines, identifying clear points where the line crosses grid intersections can make finding the slope easier.

Discover how to find the equation of a line modeled in a graph by identifying two points and calculating the slope. Learn key concepts in algebra, including slope-intercept form and the slope formula. Suitable for students in Grades 8-10.

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