teThe rate of change is referred to as the slope of the equaton hence we are asked invariably to look for the slope of the equation.
The equation given will first need to be written in its standard form. The standard form of equation of a line is y = mx+c where;
m is the slope that we need.
Next is to rewrite the given equation in the standard format.
y-6=-4(x-9)
open the parenthesis
y-6=-4x+9
add 6 to both sides
y-6+6=-4x+9+6
y = -4x+9+6
y = -4x+15
Next is to compare the resulting equation y = -4x+15 with the standard equation y = mx+c.
On comparison, it can be seen that m = -4. Hence the rate of change in this equation (slope) is -4