https://r2.erweima.ai/mathbot/image/1725709109233l45bkln9.jpg

In the image, the task is to write the equation of the line shown in **slope-intercept form** \( y = mx + b \).

From the graph:

1. The **y-intercept** \( b \) is where the line crosses the y-axis. It appears to cross at \( y = 2 \).
2. The **slope** \( m \) is the rise over run. Looking at the graph, it seems the line goes down 3 units when moving 2 units to the right, so the slope \( m \) is:

\[
m = \frac{\text{rise}}{\text{run}} = \frac{-3}{2}
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -\frac{3}{2}x + 2
\]

Would you like further details, or do you have any questions about the process?

Here are 5 related questions to explore further:
1. How do you calculate the slope if the graph is less clear?
2. What happens if the line crosses the x-axis at a different point?
3. How can you rewrite this equation in point-slope form?
4. What does a positive slope look like on a graph?
5. How does changing the y-intercept affect the graph?

**Tip:** Always check two distinct points on the graph to accurately determine the slope.

Write the equation of the line in slope-intercept form based on the graph provided.

Learn how to write the equation of a line in slope-intercept form by determining the slope and y-intercept from a graph. This algebra problem involves key concepts like slope, y-intercept, and the slope-intercept form equation y = mx + b. Suitable for students in Grades 8-10.

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