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Using x & y intercepts | C cannot be equal to 0
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Gradient - intercept method
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ax + by = c --> e.g 2x - 5y = 10
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y = mx + c
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y = 0 when solving x
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Horizontal Line
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2x - 0 = 10
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gradient = 0
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x = 5
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y = c
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x = 0 when solving y
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Vertical Line
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2(0) - 5y = 10
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gradient = undefined
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-5y = 10
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x = a
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y = 10/-5
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a --> x-intercept
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y = -2
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Gradient + y-intercept
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Gradient + a point (x1, y1)
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2 points (x1, y1) (x2, y2)
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Distance between 2 points
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Sub into equation
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Sub into equation
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1st find m
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Sub into equation
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y = mx + c
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y - y1 = m(x - x1)
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m = y2 - y1/x2 - x1
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AB = √(x2 - x1)² + (y2 - y1)²
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Example
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Example
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2nd sub into equation
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Example
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c = 5 | m = -1
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m = 2 | (2, -0.5)
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y - y1 = m(x - x1)
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A = (3, -5) | B = (-2, 1)
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y = -1x + 5
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y + 0.5 = 2(x - 2)
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Example
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AB = √(-2 - 3)² + (1 - -5)²
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y + 0.5 = 2x - 4
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(-1, 4) , (5, 2)
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AB = √(-5)² + 6²
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y = 2x - 4.5
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m = 2 - 4/3 - (-1)
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AB = √25 + 36
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m = -2/4 --> -1/2
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AB = √61
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y - 4 = -1/2(x - - 1)
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y - 4 = - 1/2x - 1/2
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y = - 1/2x + 7/2
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Middle point of a line
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Paralell Lines
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Perpendicular Lines
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Sub into equation - i.e / means divide
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Sub into equation
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Sub into equation
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M = (x1 + x2/2, y1 + y2/2)
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m1 = m2
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m1 x m2 = -1 or m2 = 1/m1
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Example
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Example - 1st find m (gradient)
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Example - 1st find m (gradient)
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(3, 5) | (2, 7)
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A (4, 13) | B (2, 9)
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A (-4, 9) | B (2, -6)
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M = 3 + 2/2, 5 + 7/2
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mAB = 9 - 13/2 - 4
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mAB = -6 - 9/2 - (-4)
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M = (5/2, 12/2)
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mAB = -4/-2
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mAB = -15/6
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M = (5/2, 6)
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mAB = 2
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mAB = -5/2
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C (0, -10) | D (15, 0)
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C (-5, 8) | D (10, 14)
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mCD = 0 - (-10)/15 - 0
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mCD = 14 - 8/10 - (-5)
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mCD = 10/15
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mCD = 6/15
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mCD = 2/3
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mCD = 2/5
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∵ mAB ≠ mCB
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2nd | sub into m1 x m2 = -1
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∴ not parralell
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-5/2 x 2/5 = -1
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-10/10 = -1
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∴ AB ⊥ CD
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