Straight line graphs

If an equations has y and/or x but no higher power (eg x², X³) then it's a straight line equation
Vertical and horizontal lines
1. x=a is a vertical line crossing a on the x-axis
2. y=a is a horizontal line through a on the y-axis
gradient
1. gradient of a line is how steep it is the larger the gradient the steeper the slope
  1. a negative gradient means the slope is downhill
2. to find the gradient change in y _________________ change in x
Example
1. Point a = (6,50) and point b = (1,10)
  1. the change in y = 50 - 10 = 40
    1. the change in x = 6-1 = 5
      1. gradient = 40/5 = 8
y = mx + c
1. m = gradient of line
2. c= y intercept
3. Example
  1. equation of this line is y = 1/2 x + 15
4. Example 2
  1. 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
    1. QUESTION: Find the equation of the straight line that passes through (-2,9) and (3,-1
      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

Resource summary

	Created by lizabeth rawson over 4 years ago