https://file.aiquickdraw.com/mathbot/file/17266993206134ydmkrmk.jpg

To solve this, we need to determine the equation of the line shown in the graph, using its slope and y-intercept or two points on the line. From the image, I can see that the question asks for the equation of the line in standard form, \(Ax + By = C\).

Here’s how we approach this:

1. **Identify Two Points on the Line**: From the graph, we can extract two distinct points that the line passes through (e.g., where it intersects grid lines).

2. **Calculate the Slope**: Using the slope formula:
   \[
   \text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
   \]

3. **Use the Slope-Intercept Form**: Start with the slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. After finding the equation in slope-intercept form, convert it to standard form \(Ax + By = C\) by rearranging the terms.

Let me analyze the graph for the specific points and values. I will get back to you shortly with the steps and answer.I've opened the image. Let's proceed by identifying two points on the line from the graph.

1. **Identify Two Points**: Looking at the grid, it seems that the line crosses through specific points. Based on the grid system, these might be \( (0, 2) \) and \( (3, 0) \).

2. **Calculate the Slope**:
   Using the points \( (0, 2) \) and \( (3, 0) \), the slope \( m \) is calculated as:
   \[
   m = \frac{0 - 2}{3 - 0} = \frac{-2}{3}
   \]

3. **Equation in Slope-Intercept Form**:
   Using the slope-intercept form, \( y = mx + b \), and substituting \( m = -\frac{2}{3} \) and the y-intercept \( b = 2 \), the equation is:
   \[
   y = -\frac{2}{3}x + 2
   \]

4. **Convert to Standard Form**:
   To convert this into standard form \(Ax + By = C\), multiply through by 3 to eliminate the fraction:
   \[
   3y = -2x + 6
   \]
   Rearranging:
   \[
   2x + 3y = 6
   \]

So, the equation of the line in standard form is:
\[
2x + 3y = 6
\]

### Do you want more details or have any questions?

Here are some related questions you might want to explore:
1. How can you find the slope if the points are not easily identifiable on a graph?
2. How do you convert a slope-intercept equation into point-slope form?
3. What does it mean when a line is vertical or horizontal in terms of slope?
4. How can you verify if a point lies on the line given its equation?
5. How would the equation change if the line were shifted vertically or horizontally?

**Tip**: When converting between different forms of a line equation, always simplify the equation to remove fractions if possible!

What is the equation of the line? Identify the values of A, B, and C in the standard form of the equation.

Learn how to find the equation of a line by identifying two points on the graph, calculating the slope, and converting the equation into standard form. Suitable for students in Grades 8-10, this problem covers key algebraic concepts including slope, y-intercept, and linear equation transformation.

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