Linear Function: Fitting Equations to Tables with Values (-1,10), (0,8), (1,6)

Given the two tables of values x and and.

These tables represent a linear function. Fit an equation of a linear function to each one.

To solve for the linear function, we need to follow these structured steps:

Step 1: Calculate the slope ($m$).

Use the points $(-1, 10)$ and $(0, 8)$. The slope $m = \frac{8 - 10}{0 - (-1)} = \frac{-2}{1} = -2$.

Step 2: Determine the y-intercept ($b$).

Use the point-slope form with the point $(0, 8)$ (since $x = 0$ is the y-intercept directly). Thus, $b = 8$.

Step 3: Write the equation of the line.

The equation fitting the table values is $y = -2x + 8$.

Therefore, the equation of the linear function is $y = -2x + 8$.