We are asked to match the graph of the equation $y = \frac{3}{4}x + 2$ with one of the four provided graph options (A, B, C, or D).

Let's break down the equation $y = \frac{3}{4}x + 2$:

1. Slope: The slope $m$ is $\frac{3}{4}$, which means that for every 4 units you move to the right along the x-axis, the y-value increases by 3 units. This gives the line a positive slope, slanting upwards as we move from left to right.
2. Y-intercept: The y-intercept is 2, meaning the line crosses the y-axis at $(0, 2)$.

Now, let's analyze each graph based on these characteristics:

• Graph A: The line passes through $(0, 2)$ and has a positive slope. It appears to rise correctly at a rate of 3 units for every 4 units moved to the right.
• Graph B: The line passes through $(0, 2)$ but has a negative slope (slanting downward), which is incorrect for this equation.
• Graph C: This graph also has a negative slope, which is not a match for $\frac{3}{4}$.
• Graph D: Similar to Graph A, the line passes through $(0, 2)$ and has a positive slope. However, the direction of the line seems incorrect for this specific slope.

Answer: Graph A matches the equation $y = \frac{3}{4}x + 2$ correctly.

Would you like more details or have further questions? Here are 5 related questions you might explore:

1. How do we graph linear equations like $y = mx + b$ in general?
2. What is the significance of the slope and y-intercept in a linear equation?
3. How would the graph change if the slope were negative?
4. How can we verify if two lines are parallel or perpendicular using their slopes?
5. What happens to the graph if we change the y-intercept value?

Tip: To quickly verify the slope on a graph, check how the line behaves between two known points like $(0, 2)$ and another point, such as $(4, 5)$, for this equation.