To determine which point is on the line represented by the equation \( y = -\frac{1}{2}x + 8 \), we can substitute the \( x \) coordinate of each point into the equation and check if the resulting \( y \) value matches the \( y \) coordinate of the point.
Let's evaluate each point:
A. (6, 5) \[ y = -\frac{1}{2}(6) + 8 = -3 + 8 = 5 \] This matches \( y = 5 \). So, point A is on the line.
B. (8, −4) \[ y = -\frac{1}{2}(8) + 8 = -4 + 8 = 4 \] This does not match \( y = -4 \). So, point B is not on the line.
C. (−8, 2) \[ y = -\frac{1}{2}(-8) + 8 = 4 + 8 = 12 \] This does not match \( y = 2 \). So, point C is not on the line.
D. (4, −6) \[ y = -\frac{1}{2}(4) + 8 = -2 + 8 = 6 \] This does not match \( y = -6 \). So, point D is not on the line.
The only point that lies on the line is A (6, 5).