Graph Analysis: Mapping Graph Points to Corresponding Data Table

Given the following graph, determine which table corresponds to the following table

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

• Step 1: Identify two points from the graph to determine the line's equation.
• Step 2: Calculate the slope $m$.
• Step 3: Use the slope to find the y-intercept $c$.
• Step 4: Write the equation of the line $Y = mX + c$.
• Step 5: Check each given table to see which one matches the line's equation.

Let's proceed with these steps:
Step 1: Looking at the graph, we pick two points, let's say $(1, 1)$ and $(2, 2)$.
Step 2: Calculate the slope: $m = \frac{2 - 1}{2 - 1} = 1$.
Step 3: Use one of the points $(1, 1)$ to find the y-intercept: since $Y = mX + c$, $1 = 1(1) + c$, hence $c = 0$.
Step 4: The line's equation is therefore $Y = X$.
Step 5: Examine the tables:

• Choice 1: $X: -1, 0, 1$ and $Y: -1, 0, 1$ matches our line $Y = X$.
• Other choices fail this test because they do not satisfy the equation.

Therefore, the correct table that corresponds to the graph is choice 1.