Answer: 24
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Step-by-step explanation:
Plug in x = 0 to find that
y = -3x+12
y = -3(0)+12
y = 12
So (0,12) is one corner of this triangular region. This is the y intercept of y = -3x+12.
Another corner is (4,0) which is the x intercept of y = -3x+12. We find this by replacing y with 0 and solving for x like so
y = -3x+12
0 = -3x+12
3x = 12
x = 12/3
x = 4
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To summarize so far, the equation y = -3x+12 has these properties
- The y intercept is (0,12)
- The x intercept is (4,0)
Those are two corner points of the triangular region. The third corner point is the origin (0,0).
Check out the diagram below.
From here, we use the area of a triangle formula to get what we're after
area = base*height/2
area = 4*12/2
area = 48/2
area = 24 square units