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!