https://file.aiquickdraw.com/mathbot/file/1726004543438atnf9wtl.jpg

To solve this problem, let's analyze the graph and compare it to the given options.

The equation of a straight line is usually written in slope-intercept form, 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: Find the slope (m)
From the graph, the line moves downward, indicating a negative slope. We can find the slope by calculating the "rise" over "run" between two points on the line. Let's choose two points:

- The line crosses through the point \( (-5, 0) \) and \( (0, -2) \).
- Slope formula: 

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 0}{0 - (-5)} = \frac{-2}{5}
\]

So the slope is \( m = -\frac{1}{3} \).

### Step 2: Find the y-intercept (b)
The y-intercept is where the line crosses the y-axis, which from the graph is \( y = -2 \).

### Step 3: Write the equation
Using the slope-intercept form \( y = mx + b \) with \( m = -\frac{1}{3} \) and \( b = -2 \), the equation of the line is:

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

### Step 4: Compare to the options
We need to rewrite this in point-slope form to match the answer choices, which are in the format:

\[
y - y_1 = m(x - x_1)
\]

From the graph, we see the line passes through \( (-5, 0) \), and substituting into point-slope form gives us:

\[
y + 2 = -\frac{1}{3}(x + 5)
\]

### Answer:
The correct answer is the first option:
\[
y + 2 = -\frac{1}{3}(x + 5)
\]

Do you have any questions or want further details? Here are 5 related questions you might want to explore:
1. How do you convert between slope-intercept form and point-slope form?
2. What are the steps to find the slope of a line from a graph?
3. How can you determine the y-intercept just by looking at the graph?
4. How do you know when to use point-slope form versus slope-intercept form?
5. Can you find the equation of a line if you're only given two points?

**Tip:** Always pick clear points from the graph when calculating the slope to avoid errors!

Which equation is best represented by the graph?

Learn how to find the equation of a straight line using the slope and point-slope form. This math problem walks through calculating the slope and identifying the equation from a graph, suitable for students in Grades 8-10.

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