Identify the Correct Equation from a Graph of a Linear Function

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

• Step 1: Identify the slope ($m$) of the line from the graph.
• Step 2: Determine the y-intercept ($b$) from the graph.
• Step 3: Match the slope and y-intercept to one of the given equations.

Now, let's work through each step:
Step 1: By observing the graph, we determine the slope ($m$). The line appears to pass through the points $(0, 4)$ and $(1, 5)$. Calculating the slope $m$ using the points, $m = \frac{5 - 4}{1 - 0} = 1$.

Step 2: The y-intercept $b$ is the point where the line crosses the y-axis, which is at $(0, 4)$. Therefore, $b = 4$.

Step 3: Using the slope-intercept form $y = mx + b$, substitute $m = 1$ and $b = 4$ to get $y = 1x + 4$, which simplifies to $y = x + 4$.

Therefore, the solution to the problem is $y = x + 4$.

From the given choices, the correct answer is choice 4: $y = x + 4$.