What is the area enclosed by the line 2x + y + 7 = 0 and the x and y axes.

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Let's find the x- and y-intercepts first.  Our equation can be rewritten

2x + y = -7

1. y-intercept.  Let x = 0. Then 2(0) + y = -7, so y = -7.

2. x-intercept. Let y = 0.  Then 2x + 0 = -7, so x = -3.5

So think about the graph:

The region contained by the line and the x- and y-axes is a right triangle with legs of length 3.5 and 7.

So the area is `1/2*3.5*7=1/2*7/2*7=49/4`

Or if you like decimals, 12.25 square units.

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