graphs

• Expanding brackets


  Multiply everything on the outside with the inside
• Solving linear equations


  1. Step 1: Isolate the variable term

  2. Step 2: Divide both sides by the coefficient of the variable
• Solving linear equations with brackets

  1. Step 1: Expand the brackets

  2. Step 2: Collect like terms

  3. Step 3: Isolate the variable
• Plotting linear graphs


  1. Step 1: Make a table of values

  2. Step 2: Plot the points

  3. Step 3: Draw the straight line
• Straight line graph


  A graph where the points form a straight line
• Determining if a point lies on a straight line

  Substitute the x-coordinate into the equation and see if the y-coordinate matches
• Plotting Graphs


  1. Step 1: Substitute x values into the equation

  2. Step 2: Plot the points on a graph

  3. Step 3: Draw a line through the points
• If a point (x,y) lies on the line y = 3x + 1


  Then y = 3x + 1
• Finding the Equation of a Straight Line

  1. Step 1: Find the gradient (m) using the formula m = (y2 - y1) / (x2 - x1)

  2. Step 2: Substitute the gradient and a point (x,y) into the equation y = mx + c to find the y-intercept (c)
• Straight line graphs have the equation y = mx + c, where m is the gradient and c is the y-intercept
• Quadratic graphs have the equation y = ax^2 + bx + c, where a, b and c are constants
• Scatter Graph


  A graph that shows the relationship between two variables
• Types of Correlation in Scatter Graphs

  • Weak positive
  • Moderate positive
  • Strong positive
  • No correlation
  • Weak negative
  • Moderate negative
  • Strong negative
• The line of best fit on a scatter graph follows the pattern of the points and keeps as many points as close as possible