To determine which graph represents the inequality $y \geq 2 - 2x$, let's break it down step by step.

Steps to Analyze the Inequality

1. Rewrite the inequality in slope-intercept form $y \geq -2x + 2$.

   • The slope $m$ is $-2$.
   • The $y$-intercept is $2$.

2. Graph the Boundary Line:

   • The boundary line is $y = -2x + 2$.
   • Since the inequality is $\geq$, the boundary line will be solid, and the shading will be above the line.

3. Identify the Correct Graph:

   • Look for a graph with a solid line with slope $-2$ (downward slope).
   • The shading should be on the side where $y$ values are greater than or equal to the line.

Correct Graph Analysis

Upon examining the options:

• The top right graph shows a solid line with a slope of $-2$ and shading above the line.

Therefore, the correct graph is the top right graph.

Need more details or clarification?

Related Questions:

1. How do you determine the slope and intercept from an equation?
2. What does the inequality symbol $\geq$ signify in a graph?
3. Why is the line solid instead of dashed for $\geq$ inequalities?
4. How do you determine which side of the line to shade?
5. Can you explain how to graph $y \geq -2x + 2$ step by step?

Tip:

For inequalities, always remember to use a solid line for $\geq$ or $\leq$, and a dashed line for $>$ or $<$.