COPY: Linear Equations and Inequalities Quiz
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Questions and Answers

What type of line is represented by a linear equation with a slope of zero?

  • Vertical line
  • Diagonal line
  • Curved line
  • Horizontal line (correct)

Which of the following statements about the slope of perpendicular lines is true?

  • Their slopes must be equal.
  • The product of their slopes equals -1. (correct)
  • The sum of their slopes equals zero.
  • The product of their slopes equals 1.

What is the proper form of an inequality for a region above the line represented by 2x + 3y = 6?

  • 2x + 3y > 6 (correct)
  • 2x + 3y ≥ 6
  • 2x + 3y < 6
  • 2x + 3y = 6

When is a boundary line included in the graph of a linear inequality?

<p>When the inequality is ≤ or ≥ (C)</p> Signup and view all the answers

How are parallel lines characterized in the context of slope?

<p>They have the same slope. (D)</p> Signup and view all the answers

Which equation represents the slope-intercept form of the line with slope 4 and y-intercept -2?

<p>y = 4x - 2 (A)</p> Signup and view all the answers

What term describes the point where a line crosses the y-axis?

<p>Y-intercept (D)</p> Signup and view all the answers

In which quadrant would the point (-3, 5) be located on the coordinate plane?

<p>Quadrant II (C)</p> Signup and view all the answers

What is calculated using the formula for distance derived from the Pythagorean theorem?

<p>The straight line distance between two points (C)</p> Signup and view all the answers

Which statement about systems of linear equations is incorrect?

<p>They must have at least one solution. (B)</p> Signup and view all the answers

Flashcards

Horizontal line

A line with a slope of zero is a horizontal line. It runs parallel to the x-axis and has no vertical change.

Perpendicular lines

Perpendicular lines have slopes that multiply to -1. This means one line's slope is the negative reciprocal of the other.

Boundary line inclusion

When the inequality is ≥ or ≤, the boundary line is included in the region. This means the points on the line are part of the solution.

Parallel lines

Parallel lines have the same slope. This means they run in the same direction and never intersect.

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Slope-intercept form

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This form makes it easy to identify the line's key characteristics.

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Y-intercept

The y-intercept is the point where the line crosses the y-axis. It is the point where x = 0.

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Quadrant II

The point (-3, 5) is located in Quadrant II of the coordinate plane. This quadrant has negative x-values and positive y-values.

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Distance formula

The distance formula, derived from the Pythagorean theorem, calculates the straight line distance between two points in a coordinate plane. It uses the difference in x-coordinates and the difference in y-coordinates.

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Systems of linear equations

Systems of linear equations can have one solution, no solutions, or infinitely many solutions. They don't always have at least one solution.

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