To determine which equation best represents the relationship between $x$ and $y$ in the graph, we need to follow these steps:

1. Check the slope (m): The slope of the line represents how much $y$ changes for a unit change in $x$. If the line rises steeply, the slope will be large, and if it rises gently, the slope will be small. In the provided equations, two different slopes are given:

   • $3$ (options A and B)
   • $\frac{1}{3}$ (options C and D)

2. Check the y-intercept (b): This is the point where the line crosses the y-axis (where $x = 0$). The given equations include:

   • $+3$ (options A and C)
   • $-1$ (options B and D)

Steps to Analyze:

• Identify the y-intercept: Check where the line crosses the y-axis. If it crosses at $y = 3$, it will be either equation A or C. If it crosses at $y = -1$, it will be either equation B or D.

• Identify the slope: To find the slope, pick two points on the graph, and calculate $\text{slope} = \frac{\Delta y}{\Delta x}$ (change in $y$ divided by change in $x$).

Based on this, we can compare the graph to the equations and find the correct match.

If you can share the graph image, I can provide a more specific answer. Would you like to upload it for further analysis?

---

1. What does the slope of a line represent in the graph?
2. How do you find the y-intercept from an equation?
3. What are some common forms of linear equations?
4. What is the process to calculate the slope between two points?
5. How does changing the slope affect the steepness of a line?

Tip: To quickly spot the slope from a graph, find two points and see how much $y$ changes for a one-unit increase in $x$.