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Write the equation of the line below in slope intercept form

To write the equation of the line in slope-intercept form \( y = mx + b \), we need to determine two key components:

1. **Slope (m)**: The slope is calculated by the formula:
   \[
   m = \frac{{\text{{rise}}}}{{\text{{run}}}}
   \]
2. **Y-intercept (b)**: This is the value where the line crosses the y-axis.

### Step 1: Calculate the Slope
Looking at the graph, we can select two points on the line. From the image, two points appear to be:
- (0, 3) where the line crosses the y-axis (this is also the y-intercept).
- (1, -1), which is another clear point on the line.

The slope is calculated as:
\[
m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{-1 - 3}}{{1 - 0}} = \frac{{-4}}{1} = -4
\]
So, the slope \( m = -4 \).

### Step 2: Determine the Y-Intercept
From the graph, we can see that the line crosses the y-axis at \( y = 3 \). Hence, the y-intercept \( b = 3 \).

### Step 3: Write the Equation
Now that we know the slope \( m = -4 \) and the y-intercept \( b = 3 \), the equation of the line is:
\[
y = -4x + 3
\]

### Final Answer:
The correct equation is \( y = -4x + 3 \), which corresponds to **option a**.

Do you have any questions or want further details on this? 

Here are 5 related questions to expand your understanding:
1. How do you calculate the slope if the points are not easily readable from a graph?
2. What is the significance of the slope in a real-world context?
3. How can you find the equation of a vertical or horizontal line?
4. What happens to the graph of the line when the slope is positive?
5. Can the slope-intercept form be converted to other forms, like the point-slope form?

**Tip:** Always pick two clear points on the line for accurate slope calculation.

Write the equation of the line below in slope intercept form.

Learn how to find the equation of a line in slope-intercept form (y = mx + b) using the given points on a graph. The problem involves calculating the slope and identifying the y-intercept. Suitable for students in Grades 8-10.

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