Short Answer 
To find the equation of a linear function using two points, first identify their coordinates (e.g., (0, 2) and (2, 0)). Then, use the slope formula to derive the equation, which simplifies to y + 2 = -x + 4.
Step 1: Identify the Points
To find the equation of a linear function, start by identifying the coordinates of the two points through which the line passes. For this example, the points are (0, 2) and (2, 0). Assign these coordinates as follows:
- (x1, y1) = (0, 2)
- (x2, y2) = (2, 0)
Step 2: Use the Slope Formula
Next, apply the slope formula, which relates the change in y to the change in x between the two points. You can set it up as:
- y – y1 = (y2 – y1)
- x – x1 = (x2 – x1)
This gives the equation: (y – 2)/(0 – 2) = (x – 0)/(2 – 0). Simplifying this leads to y – 2 = -x.
Step 3: Rewrite the Equation
Transform the obtained equation into a more standard form. From y – 2 = -x, you can add 2 to both sides to rewrite it as:
- y + 2 = -x + 4
Finally, you reach the required equation: y + 2 = -(x – 4).