Question

Which statements are true about the linear inequality y >3/4 x – 2? Check all that apply.

-The slope of the line is –2.

-The graph of y >3/4 x – 2 is a dashed line.

-The area below the line is shaded.

-One solution to the inequality is (0, 0).

-The graph intercepts the y-axis at (0, –2).

Answer 1

The answers are: B,D,E

Explanation:

I got it right and i hope this helps!

Answer 2

we have

`y > (3)/(4)x-2`

using a graph tool

see the attached figure

The solution is the shaded area

Statements

A The slope of the line is
`-2`.

The statement is False

Because the slope of the line is equal to
`(3)/(4)`

B The graph of
`y > (3)/(4)x-2` is a dashed line

The statement is True

The graph of the inequality is a dashed line, because it has no equal signs in the problem

C The area below the line is shaded

The statement is False

Because The solution is the area above the dashed line

D One solution to the inequality is
`(0,0)`

The statement is True

because

For
`x=0` and
`y=0`

substitute in the inequality

`0 > (3)/(4)*0-2`

`0 > -2` --------> the inequality is satisfied

E The graph intercepts the y-axis at
`(0,-2)`

The statement is True

see the attached figure