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pychu [463]
3 years ago
12

This graph represents −x−2y=−4 .

Mathematics
1 answer:
alekssr [168]3 years ago
6 0

Answer:

B

Step-by-step explanation:

We have the equation -x-2y=-4 and we want to find which ordered pair is in the solution -x-2y\leq -4

First, let's convert the inequality to slope-intercept form. So, we have:

-x-2y\leq-4

Add x to both sides:

-2y\leq x-4

Divide both sides by -2. Since we're dividing by a negative, we will flip the sign:

y\geq- \frac{1}{2}x+2

Therefore, our original inequality will be the same as above.

Notice that our y is <em>greater than</em> our equation.

Therefore, the shaded area will lie <em>above</em> our line.

So, any point that falls within the region above our line (in the graph) and on the line is a solution to our inequality.

(-4, 1) is below our line, so it's not a solution.

(-1, 4) is above our line. So, (-1, 4) is our answer.

(-4, -1) is again below our line. So, it's not a solution.

Finally, (4, -1) is also below our line, so it's not a solution.

Therefore, our final solution is B: (-1, 4).

Let's check this. Substitute -1 for x and 4 for y. This yields:

-(-1)-2(4)\stackrel{?}{\leq}4

Multiply:

1-8\stackrel{?}{\leq}{4}

Subtract:

-7\stackrel{\checkmark}{\leq}4

So, (-1, 4) is indeed our solution.

And we're done!

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Step-by-step explanation:

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