Parallel, perpendicular and graphs

Parallel and perpendicular

  • Parallel lines have the same gradient

  • These three lines all have a gradient of 2

  • Perpendicular means at right angles

  • If a line has gradient m then any line perpendicular to it will have the gradient -1/m

Working it out

  • Draw a sketch to find the gradient of line L
  • The line slopes down/up so the gradient is negative/positive
  • Use -1/m to calculate the gradient of P
  • If m is a fraction you can just find its reciprocal and change the sign
  • You might know P passes through() so you could use m=x and c=y to write the equation of line P
  • Check it
    • If two lines are perpendicular the product of their gradient is the equation

Mid-points

  • A line segment is a short section of a straight line
  • You can find the mid-point of a line segment if you know the coordinates of the ends
  • Coordinates of mid-point = average of x-coordinates, average of y-coordinates

Quadratics

  • Quadratic equations contain an x^2 term
  • Quadratic equations have curved graphs
  • You can draw the graph of a quadratic equation by completing a table of values

Drawing quadratic curves

  • Use a sharp pencil
  • Plot the points carefully
  • Draw a smooth curve that passes through every point
  • Label your graph
  • Shape of graph will be either u or n
  • Drawing a smooth curve
    • It’s easier to draw a smooth curve if you turn your graph paper so your hand is inside the curve
  • Check it
    • All the points on your graph should lie on the curve
    • If one of the points doesn’t fit then double check your calculations

Graphs

  • You might need to draw or interpret cubic and reciprocal graphs in your exam
  • You can use a table of values to draw any graph, but it helps if you know what the general shape of the graph is going to be

Cubic graphs

  • Graphs that contain an x^3 term and no higher powers of x are called cubic graphs

  • Here are two examples

Reciprocal graphs

  • Graphs of the form y = k/x where k is a number are called reciprocal graphs

  • Here are two examples

Tips

  • The graphs get closer and closer to the x-axis and y-axis but never touch them
  • With a cubic graph if you recognise the shape of the graph then it’s easier to tell if you’ve plotted your coordinates correctly