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Gradients of straight-line graphs

 •The gradient of a line is a measure of how steep the line is.
 •The gradient of a line can be positive, negative or zero if, moving from left to
 right, we have

    an upwards slope              a horizontal line          a downwards slope
          y                             y                          y



                         x                            x                              x
    Positive gradient              Zero gradient             Negative gradient

  •If a line is vertical its gradient cannot by specified.
Finding the gradient
      y
                                      Formula:
                                                       change in y
                                      The gradient =
                                                       change in x
                        y2 – y1
                                                          y2 – y1
                                         the gradient =
                                                          x2 – x1


              x2 – x1
                                  x
      0
What is gradient of this graph?
                                  Formula:
                      (1,4)                          change in y
                                  The gradient =
                                                     change in x

                                  Calculation:
                                  m=(-1-4)
                                     (-4-1)
                                   = -5
     (-4,-1)         (1,-1)           -5
                                   =1



                                             Total: 3/3 marks
Find the gradient of this gradient.
  s                    Formula:
                                        change in y
                       The gradient =
                                        change in x

                       m = 7-2
                           10-0
                         = 1
                            2
                                   -1
                          = 0.5cms

                  cm

                                  Total: 3/3 marks
THANK YOU

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Gradient of graph

  • 1.
  • 2. Gradients of straight-line graphs •The gradient of a line is a measure of how steep the line is. •The gradient of a line can be positive, negative or zero if, moving from left to right, we have an upwards slope a horizontal line a downwards slope y y y x x x Positive gradient Zero gradient Negative gradient •If a line is vertical its gradient cannot by specified.
  • 3. Finding the gradient y Formula: change in y The gradient = change in x y2 – y1 y2 – y1 the gradient = x2 – x1 x2 – x1 x 0
  • 4. What is gradient of this graph? Formula: (1,4) change in y The gradient = change in x Calculation: m=(-1-4) (-4-1) = -5 (-4,-1) (1,-1) -5 =1 Total: 3/3 marks
  • 5. Find the gradient of this gradient. s Formula: change in y The gradient = change in x m = 7-2 10-0 = 1 2 -1 = 0.5cms cm Total: 3/3 marks