**Parallel lines**

Starter

Find the gradient of these lines:

(a) y = 4x + 2

(b) y = x - 5

(c) y = 6 - 7x

(d) The line between (0, 4) and (3, 13)

(e) The line between (2, 1) and (6, 4)

Main Activity 1

Match the lines that parallel with each other. There may be more than one in a group.

Parallel Lines

Find the lines parallel to the given lines, passing through the given points.

(a) y = 4x - 2 (0, 5)

(b) 5 - 4x = y (0, -3)

(c) y = x - 3 (8, 9)

**L.O. - Find the equation of parallel lines.**

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2

Starter

Find the gradient of these lines:

(a) y = 4x + 2

m = 4

(b) y = x - 5

m =

(c) y = 6 - 7x

m = -7

(d) The line between (0, 4) and (3, 13)

m = 3

(e) The line between (2, 1) and (6, 4)

m =

1

2

1

2

3

4

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4

Main Activity 1

Match the lines that parallel with each other. There may be more than one in a group.

Graph A: y = 3x + 2

Graph B: y = 2x - 1, x = + 2

y

2

Graph C: 2y + 2x = 6, y = 3 - x, x = 10 - y

Graph D: 2y = x + 3, x = 2y - 4

**Key**

Examples

Examples

**Activities**

**Activity**

Answers

Answers

**Worked**

Example

Example

Parallel Lines

Find the lines parallel to the given lines, passing through the given points.

(a) y = 4x - 2 (0, 5)

y = 4x + 5

(b) 5 - 4x = y (0, -3)

y = -4x - 3

(c) y = x - 3 (8, 9)

y = x + 3

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4

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4

Parallel Lines

Lines are parallel if they have the same gradient.

(a) y = 4x - 2 2y + 8x = 6

(b) 5 - 4x = y 3y + 12x -7 = 0

(c) y = x - 3 4y - 3x = 5

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4

Parallel Lines

Lines are parallel if they have the same gradient.

(a) y = 4x - 2 2y + 8x = 6

(b) 5 - 4x = y 3y + 12x -7 = 0

(c) y = x - 3 16y - 12x = 5

3

4

No, gradient of 4

compared to -4

Yes, gradients of -4

Yes, gradients of

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4

**Worked**

Example

Example

Activity

Activity

(a) y = 4x + 7

(b) y = 3 - x

(c) y = x + 4

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