To determine which equation best represents the relationship between $x$ and $y$, we need to observe the slope and the y-intercept from the graph.

The general equation of a straight line is:

$y = mx + b$

where:

• $m$ is the slope of the line (rate of change of $y$ with respect to $x$),
• $b$ is the y-intercept (the value of $y$ when $x = 0$).

Here's how to evaluate the options:

1. Identify the slope: Look at how much $y$ increases for a given increase in $x$. The slope $m$ is given by $\frac{\Delta y}{\Delta x}$.

2. Identify the y-intercept: Check where the line crosses the y-axis (where $x = 0$).

To select the best option from:

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

you will need to provide a graph or key information about the line, such as two points on it, its slope, or y-intercept.

Would you like to upload the graph or share more details so I can help you choose the correct equation?

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Next Questions:

1. How can you calculate the slope if two points are provided from the graph?
2. What is the effect of the y-intercept on the graph of a line?
3. How does changing the slope affect the steepness of a line in a graph?
4. What is the significance of a positive vs negative slope in a graph?
5. How would the line change if the slope were doubled?

Tip: Always calculate slope carefully by choosing two clear points from the line.