Straight line graphs

Straight line graphs

1. If an equations has y and/or x but no higher power (eg x², X³) then it's a straight line equation

2. Vertical and horizontal lines

   • x=a is a vertical line crossing a on the x-axis
   • y=a is a horizontal line through a on the y-axis

3. gradient

   • gradient of a line is how steep it is the larger the gradient the steeper the slope
     • a negative gradient means the slope is downhill
   • to find the gradient change in y _________________ change in x

4. Example

   • Point a = (6,50) and point b = (1,10)
     • the change in y = 50 - 10 = 40
       • the change in x = 6-1 = 5
         • gradient = 40/5 = 8

5. y = mx + c

   • m = gradient of line
   • c= y intercept
   • Example
     • equation of this line is y = 1/2 x + 15
   • Example 2
     • If you're given two points and on a line you can find the gradient and then you can use the gradient and one of the points to find the equation of the line
       • QUESTION: Find the equation of the straight line that passes through (-2,9) and (3,-1
         • M = change in y __________ change in x
           • which is -1 - 9 __________ 3 - -2
             • which is -10 ____________ 5
               • which is -2
           • substitute one of the points into the question you just found (eg (-2,9)
             • 9 = -2 (-2) + c
               • which is 9= 4 + c
                 • c = 9-4
                   • c = 5
               • substitute back into the formula, y = -2x + 5

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