Final answer:
Points A (0, 2), B (-4, 0), and C (2, 3) all satisfy the equation x + 4 = 2y, and therefore are on the line represented by this equation. Point D (5, 2) does not satisfy the equation and is not on the line.
Step-by-step explanation:
To determine which of the following points make the linear equation x + 4 = 2y true, we need to substitute the x and y values from each point into the equation and see if they satisfy it.
- For point A (0, 2), if we substitute x = 0 and y = 2 into the equation, we get 0 + 4 = 2(2), which simplifies to 4 = 4. This is true, so point A is on the line.
- For point B (-4, 0), if we substitute x = -4 and y = 0 into the equation, we get -4 + 4 = 2(0), which simplifies to 0 = 0. This is also true, so point B is on the line.
- For point C (2, 3), if we substitute x = 2 and y = 3 into the equation, we get 2 + 4 = 2(3), which simplifies to 6 = 6. This is true, so point C is on the line.
- For point D (5, 2), if we substitute x = 5 and y = 2 into the equation, we get 5 + 4 = 2(2), which simplifies to 9 = 4. This is not true, so point D is not on the line.
All points except D make the equation true, so points A, B, and C are on the line represented by the equation x + 4 = 2y.