To graph the inequality $y > 2x$ on a coordinate plane, follow these steps:

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Step 1: Graph the boundary line $y = 2x$

The inequality $y > 2x$ is related to the line $y = 2x$, which serves as the boundary.

• Slope: The slope of the line is $2$, which means it rises 2 units for every 1 unit it moves horizontally.
• Y-intercept: The line passes through the origin $(0,0)$.

Step 2: Dashed Line

Since the inequality is strict ($y > 2x$ and not $y \geq 2x$), the boundary line $y = 2x$ is drawn as a dashed line. This indicates that the points on the line are not included in the solution.

Step 3: Shade the region above the line

• The inequality $y > 2x$ means that $y$ is greater than $2x$, so you need to shade the region above the line.
• To confirm, pick a test point not on the line (like $(0,1)$) and substitute it into $y > 2x$.
  • Substituting $(0,1)$: $1 > 2(0) \rightarrow 1 > 0$, which is true.
• This means the area above the line is the solution region.

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Graph Description:

1. Draw a dashed line through the origin with slope $2$.
2. Shade the area above the line to represent $y > 2x$.

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Would you like me to graph this inequality for you or further explain any step?

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5 Related Questions:

1. How would the graph change if the inequality were $y \geq 2x$?
2. What does the inequality $y < -3x + 2$ look like on a graph?
3. How do you determine which side of a boundary line to shade for inequalities?
4. How would you graph the inequality $y \leq -\frac{1}{2}x + 3$?
5. How do you solve a system of linear inequalities graphically?

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Tip:

For linear inequalities, always test a point (like $(0,0)$, if not on the line) to determine which region to shade.