https://file.aiquickdraw.com/mathbot/file/1725522308600i2evqwe3.jpg

To determine the equation of the line shown on the graph, let's use the slope-intercept form of a line equation, which is:

\[
y = mx + b
\]

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

### Step 1: Identify the y-intercept
From the graph, it is clear that the line crosses the y-axis at \(-1\). Therefore, \(b = -1\).

### Step 2: Determine the slope (m)
The slope can be found by using two points on the line. Let's use the points:
- \((0, -1)\) (the y-intercept)
- \((2, -4)\)

The formula for slope \(m\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the coordinates:

\[
m = \frac{-4 - (-1)}{2 - 0} = \frac{-4 + 1}{2} = \frac{-3}{2}
\]

So, the slope is \(-\frac{3}{2}\).

### Step 3: Write the equation
Now that we have the slope \(m = -\frac{3}{2}\) and the y-intercept \(b = -1\), the equation of the line is:

\[
y = -\frac{3}{2}x - 1
\]

### Final Answer:
The correct equation is:

\[
y = -\frac{3}{2}x - 1
\]

This corresponds to the first option provided in the image.

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Would you like further details or have any questions?

### Related Questions:
1. How do you find the slope between two points?
2. What is the general form of a linear equation?
3. How do you graph a line given its equation?
4. What are the differences between slope-intercept and point-slope forms?
5. How do you determine the slope of vertical or horizontal lines?

### Tip:
Always check for the y-intercept when writing the equation of a line; it helps identify the correct form quickly.

Which is the equation of the line on the graph?

Learn how to find the equation of a line from a graph using the slope-intercept form (y = mx + b). This problem involves determining the slope and y-intercept from the graph and solving the equation, suitable for students in Grades 7-9.

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