Identify the Correct Equation: Linking Values in X: -3 to 1 and Y: 0 to 4

To solve this problem, we will find the linear equation that represents the function in the table by determining the slope and y-intercept.

• Step 1: Calculate the slope $m$.
  Between two points $(-3, 0)$ and $-2, 1$, the slope is:
  $m = \frac{1 - 0}{-2 - (-3)} = \frac{1}{1} = 1$
• Step 2: Use the slope and a point to find the y-intercept $b$.
  Using the point $(-3, 0)$ and the formula $y = mx + b$, plug in the values:
  $0 = 1(-3) + b$
  $0 = -3 + b$
  $b = 3$
• Step 3: Write the equation of the line:
  $y = x + 3$

This linear equation must be consistent with all the points in the table, which it is:

• $X = -2$, $Y = 1$: $1 + 3 = 4$, so correct.
• $X = -1$, $Y = 2$: $2 + 3 = 5$, so correct.
• $X = 0$, $Y = 3$: $3$, so correct.
• $X = 1$, $Y = 4$: $4 + 3 = 7$, so correct.

The calculated equation, $y = x + 3$, matches the option given as Choice 4.

Therefore, the function that corresponds to the table is $y = x + 3$.