Question

Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded?

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

Answer 1

Answer: Third option

Above the dashed line

Explanation:

First we solve the inequality for the variable y.

`6y - 3x > 9`

`6y - 3x +3x > 9 +3x`

`6y> 9 +3x`

`y> (9)/(6) +(3)/(6)x`

`y> (3)/(2) +(1)/(2)x`

Notice that the line that limits the region is given by the equation

`y= (3)/(2) +(1)/(2)x`

The region is formed by all the points that are greater than the points that are on the line
`y= (3)/(2) +(1)/(2)x`.

Therefore the region does not include the points that are on the line, but those that are above the line. Then the line is dashed.

The answer is the third option

Answer 2

Option C is correct.

Explanation:

Option C above the dashed line is correct option.

we will graph the inequality

6y - 3x > 9

6y > 9 +3x

y >9/6 +3x/6

y > 3/2 + x/2

The line is dashed because the values are greater and not equal.

The graph is shown in the figure attached.