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3 years ago

Choose the linear inequality that describes the graph. The gray area represents the shaded region.

Mathematics

1 answer:

jek_recluse [69]3 years ago

6 0

Answer:

2x + 3y ≥ 5

Step-by-step explanation:

See the graph attached.

The bold straight line passes through the points (1,1) and (4,-1).

Therefore, the equation of the straight line will be

$\frac{y + 1}{- 1 - 1} = \frac{x - 4}{4 - 1}$

⇒ 3(y + 1) = - 2(x - 4)

⇒ 3y + 3 = - 2x + 8

⇒ 2x + 3y = 5 ............. (1)

Now, the shaded region i.e. the solution to the inequality does not include the origin(0,0).

So, putting x = 0 and y = 0 in the equation (1) we get, 0 < 5

Therefore, the inequality equation is 2x + 3y ≥ 5 (Answer)

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It states that a line with endpoint coordinates as - $(x_{1} ,y_{1} )$ and $(x_{2} ,y_{2} )$ has its mid - point at the coordinates -

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Using the Mid - Point formula, we get -

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M(- 7.5, 0.5)

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