Ask a New Question
Menu

Which linear inequality matches the given graph?

(1 point)
Responses

y≤2x+2
y less-than-or-equal-to 2 x plus 2

y>2x+2
y greater than 2 x plus 2

y<2x+2
y less than 2 x plus 2

y≥2x+2
y greater-than-or-equal-to 2 x plus 2

1 answer

To determine which linear inequality matches the given graph, you'll need to consider the following key aspects:

  1. Boundary Line: Identify the equation of the boundary line. In this case, it seems to be \(y = 2x + 2\).

  2. Type of Inequality: If the line is dashed, it indicates that the inequality does not include the line (using < or >). If the line is solid, it suggests that the inequality includes the line (using ≤ or ≥).

  3. Shading: The area that is shaded on the graph indicates where the solutions to the inequality lie. If the shading is above the line, it indicates a "greater than" inequality. If it is below the line, it suggests a "less than" inequality.

Based on these points, if the boundary line is dashed and the shading is below the line, the correct inequality would be:

  • \(y < 2x + 2\)

If the boundary line is dashed and the shading is above the line, it would be:

  • \(y > 2x + 2\)

If the line is solid and the shading is below, the correct inequality would be:

  • \(y ≤ 2x + 2\)

And if the line is solid with shading above, it would be:

  • \(y ≥ 2x + 2\)

Without seeing the actual graph, it’s impossible to choose the exact option, but you can use these guidelines to match your graph to one of the inequalities listed in your responses.