The equation written in slope-intercept form is y = (1/3)x -9
A linear equation is that which can be represented in the form of y =mx +c , m is the slope and c is the intercept.
The given equation is
y+6 = 1/3(x-9)
To determine the slope and the intercept this equation needs to be solved
y+6 = (1/3)x - 3
y = (1/3)x -9
Therefore this is the slope intercept format , here
the slope = 1/3
intercept = -9
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