Function Analysis: Identifying Y = X + 5 on a Graph

To solve this problem, we will sketch the graph of the function $Y = X + 5$.

• Step 1: Identify key points by calculating a few points for the graph:
  For $X = 0$, $Y = 0 + 5 = 5$.
  For $X = 1$, $Y = 1 + 5 = 6$.
  For $X = 2$, $Y = 2 + 5 = 7$.
• Step 2: Plot these points on a Cartesian plane.
  - The points $(0, 5)$, $(1, 6)$, and $(2, 7)$ all lie on the line with a slope of 1.
• Step 3: Draw the straight line through these points extending in both directions.

As $Y = X + 5$ represents a line with a slope of 1 and y-intercept of 5, the line will pass through all these points. Comparing this to the provided graph choices, select the graph with positive slope and y-intercept at 5.

The correct graph is choice 2, which shows a line with a slope of 1 and intercepting the y-axis precisely at 5.

Therefore, the graph that describes the function $Y = X + 5$ correctly is choice 2.