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Linear Inequalities in Two Variables quiz

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  • How do you determine if an ordered pair is a solution to a two-variable linear inequality?
    Plug the x and y values into the inequality; if the statement is true, the ordered pair is a solution.
  • What is the difference between the solution set of a linear equation and a linear inequality in two variables?
    A linear equation's solutions lie on a line, while a linear inequality's solutions form a region on the graph.
  • What type of line do you draw for the inequality y < 2x - 4?
    You draw a dashed line because the inequality symbol is '<' (less than).
  • When do you use a solid line when graphing a linear inequality?
    Use a solid line when the inequality symbol is ≤ (less than or equal to) or ≥ (greater than or equal to).
  • How do you decide which side of the line to shade when graphing a linear inequality?
    Test a point not on the line (often (0,0) if possible); if it makes the inequality true, shade that side.
  • What does the shaded region represent in the graph of a linear inequality?
    The shaded region contains all the points (ordered pairs) that satisfy the inequality.
  • If the inequality is y > 2x - 4, which region do you shade?
    Shade the region above the line y = 2x - 4.
  • What is the first step in graphing a linear inequality in two variables?
    Graph the corresponding line by replacing the inequality symbol with an equal sign.
  • How do you check if a point like (5, 3) is a solution to an inequality?
    Substitute x = 5 and y = 3 into the inequality and see if the resulting statement is true.
  • What does a dashed line indicate when graphing a linear inequality?
    A dashed line means points on the line are not included in the solution set (for < or >).
  • How is graphing x ≥ 1 on a two-dimensional graph different from a one-dimensional number line?
    On a two-dimensional graph, x = 1 is a vertical line, and you shade all points to the right of the line.
  • What shortcut can you use if the inequality is solved for y (e.g., y > mx + b)?
    If y is isolated, shade above the line for '>' or '≥', and below for '<' or '≤'.
  • Why is it helpful to test the point (0,0) when graphing inequalities?
    It's easy to substitute and often not on the line, making it a convenient test point.
  • What happens if the test point does not satisfy the inequality?
    You shade the opposite side of the line from where the test point is located.
  • How do you graph the inequality y ≤ x?
    Draw a solid line for y = x and shade the region below the line.