Coordinate Plane

• Slope of a line is defined as "rise over run" - how much it rises vertically divided by how much it runs horizontally.
  rise / run = y₁-y₂ / x₁-x₂ 
• A point where a line intersects a coordinate axis is called an intercept.
  - The x-intercept is the point on the line at which y = 0
  - The y-intercept is the point on the line at which x = 0
  Plug in 0 for x or y to find the intercepts.
• All lines can be written as equations in the form of y = mx + b, where m represents the slope of the line and b represents the y-intercept of the line.
• Finding the equation of a line:
  1) Find the slope of the line by calculating the rise over run.
      Remember that y-intercept is a point as well
  2) Plug the slope in for m in the slope-intercept equation.
  3) Solve for b, the y-intercept, by plugging the coordinates of one point into the equation. Either point's coordinates will work.
  4) Write the equation in the form of y = mx + b
• Determining which quadrants a given line passes through can be done in two ways:
  1) First, rewriting the equation in form of y = mx + b and then sketching the line
  2) Finding two points on the line by setting x and y equal to zero in the original equation. 
• The perpendicular bisector has the negative reciprocal slope of the line segment it bisects.
  1) Find the slope of the line it bisects
  2) Find the negative reciprocal by flipping the fraction and changing the sign (product must be -1)
  3) Find the midpoint of the line, by finding the midpoints of the x and y coordinates separately.
  4) To find the value of b of the perpendicular bisector substitute the coordinates of the midpoint for x and y. 
• Parallel lines have equal slopes. 
• If two lines in a plane intersect in a single point, the coordinates of that point solve the equations of both lines. To find the find the intersection point of two equations, turn them into slope-intercept form and set them equal to each other.
• When faced with an inequality in the coordinate plane:
  1) Draw the line either by converting to slope-intercept form or using the x and y intercepts
  2) Plug in a point on one side of the line. If this point makes the inequality true, that point is in the solution set. If not, the solution set is on the other side of the line.
• Distance between two points
  Square root of (x₁-x₂)²+(y₁-y₂)²
  
  Need to finish this.