I see you've uploaded an image with mathematical content. Let me analyze it and provide you with the necessary solution or explanation.

Give me a moment to examine the details!I've analyzed the image, and it contains a table of values for a linear function $y = \frac{3}{4}x + 1$. The task asks for identifying the graph corresponding to the function and determining whether it represents a proportional or non-proportional relationship.

Here are the steps to analyze it:

1. Table of Values:

   • The table shows corresponding values of $x$ and $y$ for different $x$-values. For instance, for $x = -4$, $y = -2$, and for $x = 0$, $y = 1$. These values are consistent with the equation $y = \frac{3}{4}x + 1$.

2. Graph Interpretation:

   • The graph of a linear equation like this one represents a straight line. The slope is $\frac{3}{4}$, which is positive, indicating an increasing line.
   • The $y$-intercept is 1, which means the line crosses the $y$-axis at $y = 1$.

3. Proportional vs. Non-Proportional:

   • A proportional relationship would pass through the origin (0,0). Since the $y$-intercept here is 1 (not 0), the relationship is non-proportional.

Would you like further details or clarification on this? I can also help with more questions related to linear equations!

Follow-up Questions:

1. How do you identify the slope and y-intercept from the equation of a line?
2. What is the difference between proportional and non-proportional relationships in linear functions?
3. How can you graph a linear equation using a table of values?
4. How would the graph change if the slope was negative instead of positive?
5. How do you convert the equation $y = \frac{3}{4}x + 1$ into slope-intercept form?

Tip: When identifying proportional relationships, always check if the line passes through the origin (0, 0). If it does, the relationship is proportional!