Short Answer 
The equation of the linear function passing through the points (0, 2) and (2, 0) is y + 2 = -(x – 4). This was derived by identifying the coordinates of the points and applying the slope formula to simplify the relationship between y and x.
Step 1: Identify the Points
Begin by identifying the coordinates of the two points through which the linear function passes. In this case, the points are (0, 2) and (2, 0). Assign (x1, y1) to the first point, so (x1, y1) = (0, 2), and (x2, y2) to the second point, meaning (x2, y2) = (2, 0).
Step 2: Apply the Linear Formula
Utilize the formula for the slope of a linear function: y2 – y1 / y – y1 = x2 – x1 / x – x1. By substituting the identified points into the formula, you calculate the changes in the y and x values. Replace y1 and x1 with their values to set up the equation:
- 0 – 2 = y – 2
- 2 – 0 = x – 0
Step 3: Simplify the Equation
Rearranging the equation will help simplify it further. After substituting values and simplifying the equation, you arrive at y + 2 = – (x – 4). This shows the relationship between y and x in the linear function formed by your two points.