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Does the graph represent the solution set of the system of inequalities?

y≥2x

y≥x−2

Use the image to answer the question.

The coordinate grid has x and y axes labeled from negative 5 to 5.

Select the correct answers from the lists.

(2 points)
The nonlinear graph should be a solid exponential function that approaches zero as x approaches negative infinity, and approaches infinity as x approaches infinity with shading
it.

The line should be a
line, with a slope of 1, a y-intercept of −2
, with shading
it.

So, the graph
represent the solution set of the system of inequalities.

Remaining Attempts : 3

1 answer

To determine if the graph represents the solution set of the given system of inequalities \( y \geq 2x \) and \( y \geq x - 2 \), let’s analyze each inequality:

  1. For the inequality \( y \geq 2x \):

    • The line represented by \( y = 2x \) has a slope of 2 and a y-intercept of 0.
    • Since this is a "greater than or equal to" inequality, the area above this line (including the line itself) should be shaded.

  2. For the inequality \( y \geq x - 2 \):

    • The line represented by \( y = x - 2 \) has a slope of 1 and a y-intercept of -2.
    • Similar to the previous inequality, the area above this line (including the line itself) should be shaded.

In summary:

  • The first line (\( y = 2x \)):

    • It should be a solid line (since it's "greater than or equal to").
    • It has a slope of 2 and a y-intercept of 0.
    • The area above the line should be shaded.

  • The second line (\( y = x - 2 \)):

    • It should also be a solid line (similarly "greater than or equal to").
    • It has a slope of 1 and a y-intercept of -2.
    • The area above this line should be shaded.

Now, addressing your answer choices:

  • The description you provided with the non-linear solid exponential function seems misplaced, since you are working with linear inequalities.
  • For the second line, it should be stated explicitly as a solid line, with the proper slope and y-intercept mentioned.

So, the answers for your selections would be:

  1. The first graph (associated with \( y = 2x \)):

    • "The line should be a solid line, with a slope of 2, a y-intercept of 0, with shading above it."

  2. The second graph (associated with \( y = x - 2 \)):

    • "The line should be a solid line, with a slope of 1, a y-intercept of -2, with shading above it."

Finally:

  • The graph does represent the solution set of the system of inequalities as long as it fulfills the conditions mentioned above (solidity of lines and correct shading direction).

So the filled-out statement should read: "So, the graph does represent the solution set of the system of inequalities."