Equations of straight lines

• What does a line consist of?

  All points which satisfy some equations in terms of x and/or y
• What can you do to find a missing coordinate when you know it lies on the line?

  Substitute it in to find the unknown
• What is the gradient?

  The steepness of a line, which tells us how what y changes by as x increases by 1
• What is the equation for gradient?


  Change in y/change in x
• How do you prove that 3 points lie on the same straight line?

  Prove that 2 line segments have the same gradient and that they have the same point
• What is the relationship between gradient, x and y?

  By definition, if we increase x by 1, y should increase by m
• What is the slope-intercept form of an equation of a straight line?

  y = mx + c
• What form of a straight line is y = mx + c?

  Slope-intercept form
• What is the standard form of an equation of a straight line?

  ax + by + c = 0
• What form of a straight line is ax + by + c = 0?

  Standard form
• What method do you use to find the equation of a line when one point and the gradient is given?

  Use the principal that the gradient = change in y/change in x, so put the gradient equal to y-given / x-given and rearrange to give in the form required
• What method do you use to fin the equation of a line when two points are given?

  Find the gradient with the two given points and put that equal to y-one of given coordinates/x-one of given coordinates and rearrange to give in the form required
• What is the relationship between y x and m?


  y - y1 = m(x - x1)