Question 164865
slope intercept form of equation going through the point (x1,y1) is 
(y-y1) = (x-x1)*m
where m is the slope.
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you are given the following:
m = -6
y1 = 3
x1 = 3
equation becomes
y-3 = (x-3)*-6
simplifying:
y-3 = -6x + 18
adding 3 to both sides
y = -6x + 21
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that's the equation in slope intercept form (y = mx+b)
m is the slope = -6
b is the y intercept = 21
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to prove the y intercept is correct, let x = 0.
then y = 21
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to prove this equation goes through the point (3,3), then substitute 3 for x and 3 for y.
y = -6x + 21
3 = -6(3) + 21
3 = -18 + 21
add 18 to both sides.
21 = 21
proven.
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