Determine the Corresponding Equation from Tabular Function Data

Which of the following equations corresponds to the function represented in the table?

To determine the equation corresponding to the values in the table, let's analyze the relationship between X and Y:

• Step 1: Check the change in Y with respect to X. The values show that each time X increases by 1, Y increases by 1, indicating a consistent change.
• Step 2: Calculate the slope $m$. Since the change is constant: $\Delta y / \Delta x = 1 / 1 = 1$. Thus, the slope $m = 1$.
• Step 3: Determine the y-intercept $b$. When X is 0, Y is -2. Thus, $b = -2$.
• Step 4: Formulate the equation.
Using the slope-intercept form, $y = mx + b$, where $m = 1$ and $b = -2$, the equation of the line is $y = x - 2$.

Verification with the table: - Substituting $X = -2$ yields $Y = -2 - 2 = -4$, which matches the table. - Similarly, substituting other values confirms consistency. Hence, this confirms our linear equation.

The corresponding equation for the function represented in the table is therefore $y = x - 2$.