Math Problem Statement

How will I graph ; y>4x-2 on a #line

Solution

To graph the inequality y>4x2y > 4x - 2 on a coordinate plane, follow these steps:

  1. Start by graphing the boundary line: The boundary for this inequality is the line y=4x2y = 4x - 2. This line is where yy equals 4x24x - 2. To graph it:

    • Choose two values of xx, and calculate the corresponding yy values.
      • For x=0x = 0, y=4(0)2=2y = 4(0) - 2 = -2 (Point: (0,2)(0, -2))
      • For x=1x = 1, y=4(1)2=2y = 4(1) - 2 = 2 (Point: (1,2)(1, 2))
    • Plot these points on the coordinate plane and draw the line that passes through them.
    • Use a dashed line because the inequality is strict ("greater than" but not "equal to"), so points on the line itself are not included in the solution.
  2. Shade the region above the line: The inequality is y>4x2y > 4x - 2, meaning you want the region where yy is greater than the value of 4x24x - 2. To do this:

    • Pick a test point that is not on the line, such as (0,0)(0, 0).
    • Substitute x=0x = 0 and y=0y = 0 into the inequality: 0>4(0)20>20 > 4(0) - 2 \Rightarrow 0 > -2, which is true.
    • Since the point (0,0)(0, 0) satisfies the inequality, shade the region above the dashed line.

This shaded region represents all the points where yy is greater than 4x24x - 2.

Would you like a more detailed explanation or help with another graphing concept?

Here are 5 questions that expand on this topic:

  1. How do you graph inequalities with different slopes?
  2. How does shading change if the inequality symbol is "less than" instead of "greater than"?
  3. What does the graph look like if the inequality were y4x2y \geq 4x - 2 instead of y>4x2y > 4x - 2?
  4. How do you graph inequalities involving vertical or horizontal lines?
  5. How would the graph change if the slope of the line was negative?

Tip: Always use a dashed line for inequalities that are "strict" (e.g., << or >>) and a solid line for "inclusive" inequalities (e.g., \leq or \geq).

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing Linear Inequalities

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Graphing Inequalities
Boundary Line and Shading

Suitable Grade Level

Grades 8-10