Identify the Equation: Matching Functions to Table Data

To determine the corresponding equation for the given table, follow these steps:

• Step 1: Confirm the linearity of the data by calculating the slope, $m$, using consecutive data points:
  - Between points $(-2, 0)$ and $(0, 1)$, the slope is $m = \frac{1 - 0}{0 - (-2)} = \frac{1}{2}$.
  - Between points $(0, 1)$ and $(2, 2)$, the slope is $m = \frac{2 - 1}{2 - 0} = \frac{1}{2}$.
  - Confirm the same slope $m = \frac{1}{2}$ for remaining pairs $(2, 2)$ and $(4, 3)$, $(4, 3)$ and $(6, 4)$.
• Step 2: Use one point, such as $(0, 1)$, to find the y-intercept, $b$, knowing the slope $m = \frac{1}{2}$:
  - Use the slope-intercept form: $y = mx + b$. Substituting $(0, 1)$, gives $1 = \frac{1}{2}(0) + b$, implying $b = 1$.
• Step 3: Formulate the equation: Given $m = \frac{1}{2}$ and $b = 1$, the linear function is:
  - $y = \frac{1}{2}x + 1$.
• Step 4: Compare with provided choices:

The equation $y = \frac{1}{2}x + 1$ matches choice 4. Therefore, the correct equation corresponding to the table is $y = \frac{1}{2}x + 1$.