Final answer:
The equation of the linear function is y = -3x - 32, found by calculating the slope as -3 and using the y-intercept of -32.
Step-by-step explanation:
The student is asking how to find the equation of a linear function represented in a given table with values of x and y. To determine the equation of a linear function, we need to find the slope (m) and the y-intercept (b) from the table, using the general form of a linear equation, which is y = mx + b. By examining the given values, we can calculate the slope as the change in y divided by the change in x. Then, we use one of the (x, y) pairs to find b, resulting in a complete linear equation.
From the table provided, we see a pattern: as x decreases by 2, y decreases by 6. This means the slope m is -3 (since -6 / -2 = 3), indicating that for every one unit increase in x, y decreases by 3. To find the y-intercept, we need a complete pair. Unfortunately, the pair for x = -2 is not given. We will choose x = -8 and y = -8 as our reference point. Applying it to the equation gives us -8 = -3(-8) + b, which simplifies to -8 = 24 + b. Subtracting 24 from both sides gives us b = -32. Therefore, the equation for the linear function is y = -3x - 32.