Write an equation for this linear function.
\[
f(9)=-9 \text { and } f(-6)=21
\]
\[
f(x)=-2 x+
\]

Step 1 ：We are given two points on the line, (9, -9) and (-6, 21).

Step 2 ：We can use these two points to find the slope of the line using the formula for slope, which is (y2 - y1) / (x2 - x1).

Step 3 ：Once we have the slope, we can use the point-slope form of a line to find the equation of the line. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We can use either of the given points for (x1, y1).

Step 4 ：The slope of the line is -2 and the y-intercept is 9. Therefore, the equation of the line is f(x) = -2x + 9.

Step 5 ：The equation of the line is \(\boxed{f(x) = -2x + 9}\).