Final answer:
The relationship shown is a linear function with a constant rate of change, where y decreases by 3 as x increases by 1. The corresponding linear equation is y = -3x + 12, which is option (a) from the choices given.
Step-by-step explanation:
To determine whether the relationship shows a linear function and, if so, to write the function given the sets x: 1, 2, 3, 4, 5 and y: 9, 6, 3, 0, -3, we need to look for a constant rate of change. We notice that as x increases by 1, y decreases by 3. This is a constant rate of change which suggests a linear relationship. The slope (m) of the line would be -3 (the change in y for a unit change in x), and we need to find the y-intercept (b).
If we use the first coordinate pair (1, 9), we can substitute x and y into the linear equation format y = mx + b to find the y-intercept:
9 = (-3)(1) + b
b = 9 + 3
b = 12
So the linear equation that represents this relationship is y = -3x + 12, which corresponds to option (a).