Final answer:
The equation of the linear function that passes through the point (9, 11/2) and has a slope of -5/6 is y = -5/6x + 11/2.
Step-by-step explanation:
To write the equation of a linear function, we can use the point-slope form, which is y - y1 = m(x - x1). Here, the point is (9, 11/2) and the slope is -5/6. Let's substitute the values into the equation:
y - 11/2 = (-5/6)(x - 9)
Next, let's simplify the equation:
y - 11/2 = -5/6x + 15/2
To isolate y, we can add 11/2 to both sides:
y = -5/6x + 11/2
Therefore, the equation of the linear function that passes through the point (9, 11/2) and has a slope of -5/6 is y = -5/6x + 11/2.