gradient of a line getting ready for a-level€¦ · gradient of a line (1,1) the gradient measures...

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Getting ready for A-Level... Gradient of a line Getting ready for A-Level Maths... What you need... Your brain and attention A pen and paper Can do attitude

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Page 1: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Getting ready for A-Level...Gradient of a line

Getting ready for A-Level Maths...

What you need...– Your brain and attention– A pen and paper– Can do attitude

Page 2: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Page 3: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

Page 4: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

Page 5: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradient

Page 6: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradient

Page 7: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradient

Page 8: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradient

Page 9: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradient

Page 10: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradient

Page 11: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradient

Page 12: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradients can be positive, negative, zero, or undefined.

Gradient

Page 13: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

(1,1)

The gradient measures the steepness of a line.

i.e. How far you go vertically for each 1 unit you go to the right.

Gradients can be positive, negative, zero, or undefined.

Gradient

y2-y1x2-x1

m =

Given two points (x1,y1) and (x2,y2), the gradient between them can be found using the formula:

Formula

change in yGradient=change in x

Page 14: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

x

y

x

y

Page 15: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

x

y

x

y

Page 16: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

x

y

x

y

Page 17: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

x

y y

x

Page 18: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

x

y y

x

Page 19: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Find the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

My turn Your turnFind the gradient, m, of the line shown on the graph below. Give your answer in its simplest form.

3

6

Ox

y

2

8

Ox

y

Page 20: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Find the gradient, m, of the line segments between the points (1,2) and (7,20). Give your answer in its simplest form.

My turn Your turnFind the gradient, m, of the line segments between the points (2,3) and (6,23). Give your answer in its simplest form.

Page 21: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a line

Find the gradient, m, of the line segments between the points (1,-8) and (3,-5). Give your answer in its simplest form.

My turn Your turnFind the gradient, m, of the line segments between the points (2,-6) and (5,7). Give your answer in its simplest form.

Page 22: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

A(-3,6) and P(a,2a) are two points, where a is a constant. The gradient, m, of AP is 4. Solve for a.

A(-1,3) and P(a,5a) are two points, where a is a constant. The gradient, m, of AP is 7. Solve for a.

Gradient of a lineMy turn Your turnExam Q Exam Q

Page 23: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

A(-2,4) and P(a,b) are two points, where a and b are constants. The gradient, m, of AP is 3. Find an expression for b in terms of a.

A(-1,6) and P(a,b) are two points, where a and b are constants. The gradient, m, of AP is 4.

Find an expression for b in terms of a.

Gradient of a lineMy turn Your turnExam Q Exam Q

Page 24: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a lineReview Exercise Part 1

2.1.

Find the gradient, m, of the lines shown on the following graphs.Give your answers in their simplest form where appropriate.

3.

x

y y y

x x

Page 25: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a lineReview Exercise Part 2

5.4.

Find the gradient, m, of the lines shown on the following graphs.Give your answers in their simplest form where appropriate.

y y

x x

Page 26: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a lineReview Exercise Part 3

7.

6.

Find the gradient, m, of the line segments between the points (1,4) and (5,28). Give your answer in its simplest form.

8. Find the gradient, m, of the line segments between the points (2,-9) and (5,-4). Give your answer in its simplest form.

Find the gradient, m, of the line shown on the graph. Give your answer in its simplest form.

4

12

Ox

y

Page 27: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a lineReview Exercise Part 1 (Answers)

2.1.

Find the gradient, m, of the lines shown on the following graphs.Give your answers in their simplest form where appropriate.

3.

51m = 4 m = 5 m =

x

y y y

x x

Page 28: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a lineReview Exercise Part 2 (Answers)

5.4.

Find the gradient, m, of the lines shown on the following graphs.Give your answers in their simplest form where appropriate.

52m = 3

4m = -

y y

x x

Page 29: Gradient of a line Getting ready for A-Level€¦ · Gradient of a line (1,1) The gradient measures the steepness of a line. i.e. How far you go vertically for each 1 unit you go

Gradient of a lineReview Exercise Part 3 (Answers)

7.

6.

Find the gradient, m, of the line segments between the points (1,4) and (5,28). Give your answer in its simplest form.

35

8. Find the gradient, m, of the line segments between the points (2,-9) and (5,-4). Give your answer in its simplest form.

Find the gradient, m, of the line shown on the graph. Give your answer in its simplest form.

4

12

Ox

y

m = -3

m = 6

m =