Linear Function: Match the Equation to Table Values (-2,4), (-1,2), (1,-2)

Below is a table containing values for x and y. This tables represents a linear function.

Choose the equation that corresponds to the function.

To find the equation of the linear function corresponding to the given table, follow these steps:

• Step 1: Identify Points
  We have three points from the table: $(-2, 4)$, $(-1, 2)$, and $(1, -2)$.
• Step 2: Calculate the Slope
  The slope $m$ can be calculated using any two points. Choosing $(-2, 4)$ and $(-1, 2)$:
  $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 4}{-1 - (-2)} = \frac{-2}{1} = -2$.
• Step 3: Verify Linear Relationship
  Using $(x, y)$ pairs, check another pair such as $(-1, 2)$ and $(1, -2)$:
  $m = \frac{-2 - 2}{1 - (-1)} = \frac{-4}{2} = -2$.
• Step 4: Select the Correct Equation
  The slope is $-2$, and since a linear function typically can be formatted as $y = mx + b$, we can see if $b = 0$ by trying one of the equations $y = -2x$ given in the choices. Let’s check:
  For $x = -2$: $y = -2(-2) = 4$. Matches.
  For $x = -1$: $y = -2(-1) = 2$. Matches.
  For $x = 1$: $y = -2(1) = -2$. Matches.

Therefore, the equation that corresponds to the function is $y = -2x$.