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!