https://file.aiquickdraw.com/mathbot/file/172722767895973rgdl35.jpg

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!

Learn how to determine the equation of a line passing through the points (-6, 3) and (0, 1). This problem explores concepts such as slope calculation and the slope-intercept form of a line equation. Suitable for students in Grades 8-10.

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