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Systems of Linear Inequalities quiz

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  • What is the first step when graphing a system of linear inequalities?
    The first step is to graph each inequality's boundary line, treating the inequality as if it were an equation.
  • How do you decide whether to use a solid or dashed line when graphing an inequality?
    Use a solid line for ≤ or ≥ and a dashed line for < or >.
  • What does the overlapping shaded region represent in a system of inequalities?
    The overlapping shaded region is the solution set where all inequalities are true at the same time.
  • How can you determine which side of the boundary line to shade for an inequality?
    Use a test point, such as (0,0), and substitute it into the inequality to see if it makes the statement true.
  • What should you do if your test point makes the inequality true?
    Shade the side of the line that includes the test point.
  • What should you do if your test point makes the inequality false?
    Shade the side of the line that does not include the test point.
  • Why is slope-intercept form useful when graphing inequalities?
    Slope-intercept form (y = mx + b) makes it easier to identify the y-intercept and slope for graphing.
  • What does it mean if there is no overlapping region after shading all inequalities?
    It means there is no solution to the system of inequalities.
  • How do you graph the line for y ≤ -x + 4?
    Plot the y-intercept at 4, use a slope of -1, and draw a solid line.
  • How do you graph the line for y > 2x + 1?
    Plot the y-intercept at 1, use a slope of 2, and draw a dashed line.
  • What is the purpose of using different colors or shading styles when graphing systems of inequalities?
    Different colors or shading styles help distinguish the solution regions for each inequality.
  • What is a test point, and why is it used?
    A test point is a coordinate (like (0,0)) used to determine which side of the boundary line to shade.
  • What do you do after shading the regions for all inequalities in the system?
    Highlight or shade the area where all shaded regions overlap, as this is the solution.
  • Can you use any point as a test point when shading for an inequality?
    Yes, as long as the point is not on the boundary line.
  • What should you do if the equations are not in slope-intercept form before graphing?
    Manipulate the equation to get it into slope-intercept form (y = mx + b) before graphing.