Identify the Function Graph Passing Through (1/2, 9/2)

To solve this problem, we'll follow these steps:

• Step 1: Identify the given point and convert to uniform representation.
• Step 2: Substitute the point into each equation to find which is satisfied.

Now, let's work through each step:
Step 1: The problem provides the point $\left(\frac{1}{2}, 4\frac{1}{2}\right)$, which can be expressed as $\left(\frac{1}{2}, \frac{9}{2}\right)$.
Step 2: We will substitute $x = \frac{1}{2}$ and $y = \frac{9}{2}$ into each equation:

Choice 1: $2 - y = 5x$

Substitute: $2 - \frac{9}{2} = 5 \times \frac{1}{2}$
Simplify: $-\frac{5}{2} = \frac{5}{2}$. This equation is not satisfied.

Choice 2: $5x = y - 2$

Substitute: $5 \times \frac{1}{2} = \frac{9}{2} - 2$
Simplify: $\frac{5}{2} = \frac{9}{2} - \frac{4}{2} = \frac{5}{2}$. This equation is satisfied.

Therefore, the solution to the problem is $5x = y - 2$, which corresponds to choice 2.