Ask a New Question
Menu

Use the image to answer the question.

A solid line drawn on a coordinate plane slopes steeply upward from bottom left to top right. The part of the plane to the right of the line is shaded. Both axes range from negative 10 to 10 in unit increments.

Which linear inequality matches the given graph?

(1 point)
Responses

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

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

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

y<2x+2
y less than 2 x plus 2
Skip to navigation

1 answer

To determine the correct linear inequality that corresponds to the given graph, we need to analyze the slope and the shading of the line.

  1. Identify the Slope and Y-Intercept: The slope of the line is steep and appears to be 2 (rise over run), and it crosses the y-axis at +2. Therefore, the equation of the line is likely \(y = 2x + 2\).

  2. Shading: Since the part of the plane to the right of the line is shaded, this means the inequality must represent all points above the line, which is indicative of a "greater than" condition.

  3. Choosing the Correct Inequality:

    • The inequality would be \(y > 2x + 2\) if the line itself is not included (which corresponds to the region above the line).
    • If the line is included, it would be \(y \geq 2x + 2\).

Since we only want points above and to the right of the line, and assuming the line is not drawn as a dashed line (indicating inclusion), the correct choice is:

y > 2x + 2

So the answer is: y > 2x + 2.