Question

This graph represents −x−2y=−4 .

Which ordered pair is in the solution set of −x−2y≤−4 ?

A. (−4, 1)

B. (−1, 4)

C. (−4, −1)

D. (4, −1)

Answer 1

B

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- (1)/(2)x+2`

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

Notice that our y is greater than our equation.

Therefore, the shaded area will lie above 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!