T Madas T Madas The formal definition of

The formal definition of the gradient is: difference in y dy dif in y

Two points P and Q are marked on the grid below. 1. Mark on

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The formal definition of the gradient is: difference in y dy dif in y gradient = = = difference in x dx dif in x 6 gradient = 6 = 2 3 3 © T Madas

The formal definition of the gradient is: difference in y dy dif in y gradient = = = difference in x dx dif in x 4 1 4 = 0. 5 = gradient = 2 8 8 © T Madas

The formal definition of the gradient is: difference in y dy dif in y gradient = = = difference in x dx dif in x 5 gradient = 5 ≈ 0. 71 7 7 © T Madas

The formal definition of the gradient is: difference in y dy dif in y gradient = = = difference in x dx dif in x 1 -4 = -0. 5 gradient = = 2 8 -4 8 © T Madas

The formal definition of the gradient is: difference in y dy dif in y gradient = = = difference in x dx dif in x 6 -6 ≈ -0. 86 gradient = = 7 7 -6 7 © T Madas

The formal definition of the gradient is: difference in y dy dif in y gradient = = = difference in x dx dif in x Find the gradient of the line joining the points (3, 5) and (7, 8) dif in y 8– 5 gradient = = dif in x 7– 3 5– 8 = 3– 7 3 = 4 3 -3 = = 4 -4 © T Madas

The formal definition of the gradient is: difference in y dy dif in y gradient = = = difference in x dx dif in x Find the gradient of the line joining the points (3, 2) and (9, -1) dif in y -1 – 2 gradient = = dif in x 9– 3 = -3 1 = = 6 2 3 1 2 – (-1) = = -6 2 3– 9 © T Madas

The formal definition of the gradient is: difference in y dy dif in y gradient = = = difference in x dx dif in x Find the gradient of the line joining the points (-6, -2) and (8, 0) dif in y 2 1 0 – (-2) gradient = = dif in x 14 7 8 – (-6) = -2 – 0 -6 – 8 = -2 1 = -14 7 © T Madas

y 8 6 4 2 -10 -8 -6 -4 -2 2 -2 4 6 8 10 x -4 -6 Work out the gradient of these line segments -8 © T Madas

y 8 6 4 5 2 -10 -8 -6 -4 -2 2 -2 5 4 6 8 10 x -4 -6 Work out the gradient of these line segments 1 -8 © T Madas

y 8 6 4 6 2 3 -12 -10 -8 -6 -4 -2 2 -2 4 6 8 10 x -4 -6 Work out the gradient of these line segments -2 -8 © T Madas

y 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 -2 10 x -4 6 -6 Work out the gradient of these line segments 2 -8 3 © T Madas

y 8 6 4 2 -10 -8 -6 -4 -2 2 -2 -4 4 7 6 8 10 x 1 -6 Work out the gradient of these line segments -7 -8 © T Madas

y 8 6 4 2 -10 -8 -6 -4 -2 2 4 -2 6 8 10 x -4 6 -6 Work out the gradient of these line segments 2 -8 3 © T Madas

y 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 -2 -4 -6 Work out the gradient of these line segments -1 -8 8 10 x 5 5 © T Madas

y 8 6 4 2 -10 -8 6 -6 -4 1 -2 2 -2 4 6 8 10 x -4 -6 Work out the gradient of these line segments -8 © T Madas

y 8 6 4 2 -10 -8 -6 -4 -2 2 -2 12 4 6 8 10 x -4 -6 Work out the gradient of these line segments -4 -8 3 © T Madas

y 8 6 4 2 -10 -8 -6 4 -4 3 -2 2 -2 4 6 8 10 x -4 -6 Work out the gradient of these line segments -8 © T Madas

y 8 6 4 2 -10 -8 -6 -4 -2 9 3 2 -2 4 6 8 10 x -4 -6 Work out the gradient of these line segments 3 -8 © T Madas

-12 y 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 x -4 -6 -8 Work out the gradient of these line segments © T Madas

-12 y 8 6 -7 6 1 4 2 -10 -8 -6 -4 -2 2 -2 4 6 8 2 10 x -4 -6 3 -1 -8 Work out the gradient of these line segments © T Madas

Two points P and Q are marked on the grid below. 1. Mark on the grid as point M, the midpoint of PQ. 2. Work out the gradient of PQ. 3. Construct the perpendicular bisector of PQ by considering gradients of lines. y 12 The gradient of PQ is 11 2 4 = 3 6 10 9 8 We can also use the formal definition of the gradient: P (2, 7) 7 6 5 dif in y dif in x 3 – 7 = 8 – 2 gradient = M 4 4 3 Q (8, 3) 6 2 1 0 x 1 2 3 4 5 -4 6 2 = 3 = 6 7 8 9 10 11 12 © T Madas

Two points P and Q are marked on the grid below. 1. Mark on the grid as point M, the midpoint of PQ. 2. Work out the gradient of PQ. 3. Construct the perpendicular bisector of PQ by considering gradients of lines. y 12 The gradient of PQ is 11 the gradient of a line which is 3 perpendicular to PQ is 2 10 9 8 P (2, 7) 7 2 4 = 3 6 M 5 2 4 Q (8, 3) 3 2 1 0 x 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas

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