GRAPHING LINEAR FUNCTIONS

Graphing Straight Lines

This presentation looks at two methods for graphing a line.

1. By finding and plotting points

2. Using the gradient and the y-intercept where y = mx + b

m is the gradient

b is the

y-intercept

1. Graphing Straight Lines by plotting points

y = 2x – 1 y

x1 2 3 4 5-1-2-3

123456

-1-2-3-4

Choose values for x and find the corresponding value for y

x = 1, y = 2(1) - 1 = 1 •

x = 2, y = 2(2) - 1 = 3

•

x = -1, y = 2(-1) - 1 = - 3 •

Connect the points

This information is often presented in table form

xy

11

23

–1–3

y = – x + 2 y

x1 2 3 4 5-1-2-3

123456

-1-2-3-4

Choose values for x and find the corresponding value for y

x = 1, y = -(1) +2 = 1 •

x = 2, y = -(2) +2 = 0 •

x = -1, y = -(-1) +2 = 3

•

x = 3, y = -(3) +2 = -1

•

Connect the points

1. Graphing Straight Lines by plotting points

2. Graphing Straight Lines by using the gradient and the y-intercept

y

x1 2 3 4 5-1-2-3

123456

-1-2-3-4

•

y = 2x – 3

m =

y-intercept =

2

– 3

Place a point at the y-intercept

•A gradient of 2 is a rise of 2 over a run of 1

This gives us the point (1, –1)

Connect the points

2. Graphing Straight Lines by using the gradient and the y-intercept

y

x1 2 3 4 5-1-2-3

123456

-1-2-3-4

•

y = – 4x + 2

m =

y-intercept =

– 4

2

Place a point at the y-intercept

•

A gradient of –4 is a drop of 4 over a run of 1

This gives us the point (1, –2)

Connect the points

2. Graphing Straight Lines by using the gradient and the y-intercept

y

x1 2 3 4 5-1-2-3

123456

-1-2-3-4 •

y = – x – 3

m =

y-intercept =

– 1

– 3

Place a point at the y-intercept

•A gradient of –1 is a drop of 1 over a run of 1

This gives us the point (1, –4)

Connect the points

2. Graphing Straight Lines by using the gradient and the y-intercept

y

x1 2 3 4 5-1-2-3

123456

-1-2-3-4

•m =

y-intercept = 2

Place a point at the y-intercept

•

This gives us the point (3, 4)

Connect the points

23

2 xy

3

2

A gradient of is a rise of 2 over a run of 3

3

2

Re-arranging equations to read the gradient and the y-intercept

Remember the general form of a straight line is y = mx + b

7 yxExample 1 Subtract x from both sides

xy 7 Rearrange so that the x term is first

7 xy

Therefore, the gradient is – 1 and the y-intercept is 7.

y = mx + b

23 yxExample 2 Subtract 3x from both sides

xy 32 Rearrange so that the x term is first

23 xy

Therefore, the gradient is – 3 and the y-intercept is – 2

y

x1 2 3-1-2-3-4

12345

-1-2-3-4-5

•

•

y = mx + b

14 yxExample 3 Subtract 4x from both sides

xy 41 Rearrange so that the x term is first

14 xy

Therefore, the gradient is 4 and the y-intercept is – 1

y

x1 2 3-1-2-3-4

12345

-1-2-3-4-5

•

•

Multiply both sides by – 1

14 xy

y = mx + b

52 xyExample 4 Add x to both sides

xy 52 Rearrange so that the x term is first

52 xy

y

x1 2 3 4-1-2-3

1

2

3

4

5

-1

-2

••

Divide both sides by 2

2

5

2

1 xy

Therefore, the gradient is

and the y-intercept is 2.52

1

y = mx + b

823 xyExample 5 Add 2x to both sides

xy 283 Rearrange so that the x term is first

823 xy

y

x1 2 3 4-1-2-3

1

2

3

4

5

-1

-2

•

•

Divide both sides by 3

3

8

3

2 xy

Therefore, the gradient is and

the y-intercept is 3

2

3

8

y = mx + b

624 yxExample 6 Subtract 4x from both sides

xy 462 Rearrange so that the x term is first

642 xy

y

x1 2 3 4-1-2-3

1

2

3

4

5

-1

-2

•

•

Divide both sides by 2

32 xy

Therefore, the gradient is – 2 and the y-intercept is 3

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