https://file.aiquickdraw.com/mathbot/file/1730386747683x6jt03uv.jpg

To determine the equation of the linear function represented by this graph, let's analyze the line’s slope and y-intercept:

1. **Identify the y-intercept**: The graph intersects the y-axis at \( y = -1 \). This indicates the y-intercept \( b \) of the line is -1.

2. **Calculate the slope (m)**: 
   - Pick two points on the line to calculate the slope. One clear pair is \((0, -1)\) (the y-intercept) and another point is \((2, -4)\).
   - Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):
     \[
     m = \frac{-4 - (-1)}{2 - 0} = \frac{-3}{2}
     \]

3. **Formulate the equation**: With a slope \( m = -\frac{3}{2} \) and y-intercept \( b = -1 \), the equation of the line is:
   \[
   y = -\frac{3}{2}x - 1
   \]

4. **Compare with the options**: The correct option that matches \( y = -\frac{3}{2}x - 1 \) is the second choice.

**Answer**: The correct answer is:
\[
y = -\frac{3}{2}x - 1
\]

Would you like a further breakdown of any step?

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Here are 5 related questions to expand your understanding:

1. How do you determine the slope from a graph if the points are not clearly labeled?
2. What is the significance of the y-intercept in the context of linear functions?
3. How can you determine if a line is increasing or decreasing based on its slope?
4. How would you write the equation if the slope were positive but the y-intercept remained the same?
5. How can the slope-intercept form help in quickly graphing a linear function?

**Tip**: The slope tells you how steep the line is and in which direction it moves (upwards or downwards) as \( x \) increases.

The graph of a linear function is shown on the grid. Which equation is best represented by this graph?

Determine the equation of a linear function based on a given graph. This solution includes step-by-step identification of the slope and y-intercept using points from the graph. Suitable for students in Grades 8-10.

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