Question

Which correctly describes how the graph of the inequality −4y − x ≥ 7 is shaded?

Above the solid line
Below the solid line
Above the dashed line
Below the dashed line

Answer 1

Answer: Below the solid line

Explanation:

-4y - x ≥ 7

add x to both sides

-4y ≥ x + 7

divide by -4 on both sides

y ≤ -1/4x - 7/4 = (1.75)

Take the origin (0,0) and substitute it for the variables

y(0) ≤ -1/4(0) - 7/4

0 ≤ -7/4 = (1.75)

This statement is false, so you would shade on a graph, below the solid line, since this is where the origin would not be.

The line would be solid because the < is underlined.

Answer 2

Below the solid line

Explanation:

Given inequality,

- 4y - x ≥ 7

Related equation,

- 4y - x = 7

Which is a line passes through (-7, 0) and (0, -1.75),

Since, '≥' represents the solid line,

Thus, join the points (-7, 0) and (0, -1.75) by dotted line,

-4(0) - (0) ≥ 7

⇒ 0 - 0 ≥ 7

⇒ 0 ≥ 7

Which is a false statement.

Hence, the correct option is,

'Below the solid line'