It seems like you're referring to a graph that shows a linear relationship between $x$ and $y$. Since I can't see the graph directly, let me guide you through the process of determining which equation best fits.

Steps to identify the correct equation:

1. Identify the slope ($m$): Look at how much $y$ increases or decreases as $x$ increases by 1 unit. This will give you the slope. The options suggest slopes of 3 and 13, so check whether the rise over run in the graph matches one of these.

2. Identify the y-intercept ($b$): This is where the line crosses the $y$-axis (where $x = 0$). From the choices, the $y$-intercepts provided are $3$ and $-1$.

Matching equations to the graph:

The equation of a straight line is generally given by: $y = mx + b$ where $m$ is the slope and $b$ is the $y$-intercept.

• Option A: $y = 3x + 3$ (slope $3$, y-intercept $3$)
• Option B: $y = 3x - 1$ (slope $3$, y-intercept $-1$)
• Option C: $y = 13x + 3$ (slope $13$, y-intercept $3$)
• Option D: $y = 13x - 1$ (slope $13$, y-intercept $-1$)

Now, if you can identify the slope and y-intercept from the graph, you can match it to one of these equations.

If you want me to solve it further, you can upload the image, and I’ll analyze the graph for you.

Would you like to upload the graph, or do you have any questions about this approach?

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Follow-up Questions:

1. How do you find the slope from a graph of a straight line?
2. What is the general formula for a linear equation?
3. Can two different lines have the same slope but different y-intercepts?
4. Why is the y-intercept important in identifying the correct equation?
5. How does the steepness of a line relate to its slope?

Tip:

To find the slope quickly, you can pick two points on the line, find the difference in $y$-values (rise) and divide it by the difference in $x$-values (run).