From the image, I can see a line passing through two points on the coordinate plane. To write the equation of the line, we need the slope $m$ and the y-intercept $b$ of the line.

Step 1: Identify Two Points on the Line

Looking at the graph:

• One point appears to be $(-6, 3)$
• Another point is at $(0, 1)$, which is the y-intercept.

Step 2: Calculate the Slope

The formula for slope $m$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using points $(-6, 3)$ and $(0, 1)$:

$m = \frac{1 - 3}{0 - (-6)} = \frac{-2}{6} = -\frac{1}{3}$

Step 3: Write the Equation

Since we already know that the y-intercept $b = 1$ (from the point $(0, 1)$), the equation of the line in slope-intercept form $y = mx + b$ is:

$y = -\frac{1}{3}x + 1$

This is the equation of the line.

Would you like further details on this process or have any other questions?

Here are some related questions to explore further:

1. What is the significance of the slope in the equation of a line?
2. How do you convert a line equation from slope-intercept form to standard form?
3. What would the line look like if the slope were positive?
4. How do we interpret the y-intercept in the context of real-world problems?
5. How can we determine the x-intercept from this equation?

Tip: Always plot at least two points when graphing a line to ensure accuracy!