Mathematics

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).

2 Answer

  • we have

    [tex]y > \frac{3}{4}x-2[/tex]

    using a graph tool

    see the attached figure

    The solution is the shaded area

    Statements

    A The slope of the line is [tex]-2[/tex].

    The statement is False

    Because the slope of the line is equal to [tex]\frac{3}{4}[/tex]

    B The graph of [tex]y > \frac{3}{4}x-2[/tex] 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 [tex](0,0)[/tex]

    The statement is True

    because

    For [tex]x=0[/tex] and [tex]y=0[/tex]

    substitute in the inequality

    [tex]0 > \frac{3}{4}*0-2[/tex]

    [tex]0 > -2[/tex] -------->  the inequality is satisfied

    E The graph intercepts the y-axis at [tex](0,-2)[/tex]

    The statement is True

    see the attached figure


  • Answer:

    The answers are: B,D,E

    Step-by-step explanation:

    I got it right and i hope this helps!

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