Math

• Slope of a line


  The ratio of the change in vertical distance (rise) to the change in horizontal distance (run)
• The higher the absolute value of a slope is, the steeper the line becomes
• Horizontal line


  Has no slope or with the slope 0
• Vertical line


  Has an undefined slope
• Positive slope


  The line is increasing from left to right
• Negative slope


  The line is decreasing from left to right
• Finding the slope of a line given its graph

  1. Rise (change in vertical distance)

  2. Run (change in horizontal distance)

  3. Substitute into formula: slope = rise/run
• Parallel lines


  • Have the same slope
• Perpendicular lines


  • Have slopes which are negative reciprocals of each other
• A slope is the ratio of the change in vertical distance (rise) to the change in horizontal distance (run). It is usually denoted by the variable m.
• The higher the absolute value of a slope is, the steeper the line becomes.
• A horizontal line has no slope or with the slope 0.
• A vertical line has an undefined slope.
• A positive slope means that the line is increasing from left to right.
• A negative slope means that the line is decreasing from left to right.
• To find the slope of a line given its graph, we use the formula slope = rise/run.
• Given the coordinates of two points (x1, y1) and (x2, y2), to find the slope of the line determined by these two points, we use the formula slope = (y2 - y1) / (x2 - x1).
• Two lines that are parallel have the same slope.
• Two lines that are perpendicular have slopes which are negative reciprocals of each other.
• Rectangular coordinate system


  A two-dimensional grid used to locate the position of a place
• Rectangular coordinate system


  • Uses easting (eastward-measured distance) and northing (northward-measured distance) to locate a specific place
• Rectangular coordinate system


  Locating a particular place
• Rectangular coordinate plane


  Composed of two number lines perpendicular to each other, also called the Cartesian coordinate plane
• 1. axis


  The horizontal number line in the rectangular coordinate plane, also called the axis of abscissa
• 1. axis


  The vertical number line in the rectangular coordinate plane, also called the axis of ordinate
• Origin


  The point where the X-axis and the Y-axis in the rectangular coordinate plane intersect
• Quadrants


  The four regions into which the intersecting X-axis and Y-axis divide the rectangular coordinate plane
• Ordered pair represented by the coordinates of X and Y, called an ordered pair (X,Y)
• Determining coordinates

  • Determine the ordered pair that describes the given point on the rectangular coordinate plane
• The rectangular coordinate plane is composed of two number lines perpendicular to each other, also called the Cartesian coordinate plane
• The X-axis is the horizontal number line in the rectangular coordinate plane, also called the axis of abscissa
• The Y-axis is the vertical number line in the rectangular coordinate plane, also called the axis of ordinate
• The origin is the point where the X-axis and the Y-axis in the rectangular coordinate plane intersect
• Signs of the coordinates in each quadrant

  • Quadrant I: +,+
  • Quadrant II: -,+
  • Quadrant III: -,-
  • Quadrant IV: +,-