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## Straight Line Graphs

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### Straight Line Graphs

### Starter Questions

### Straight Line Graphs

### Straight Line Graphs

### Starter Questions

### The Gradient of a Line

### The Gradient

### The Gradient

### The Gradient of a Line

### Starter Questions

### The Gradient of a Line

### Starter Questions

### Starter Questions

### Straight Line Equation

Drawing Straight line graphs

The gradient

The gradient from coordinates

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The y intercept y = mx + c

Other forms / rearranging equation

Created by Mr.Lafferty Maths Dept

Q1. A house is valued at £50 000.

Calculate its value after 4 years, if it appreciates by 5% each year.

Q2. Calculate 3.36 x 70 to 2 significant figures.

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Q3. Calculate the volume of a cylinder with radius 5cm

and height 100 cm.

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Learning Intention

Success Criteria

- To draw graphs by using a coordinate table

- Understand the key points of drawing a straight line graph

- Be able to plot a straight line graph

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Created by Mr.Lafferty Maths Dept

10

9

8

7

6

5

4

3

2

1

x

0

-10

1

2

3

4

5

6

7

9

10

-9

-8

-6

-4

-3

-2

8

-7

-5

-1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Drawing Straight Line Graphs y = mx + c

y = x

x

y

0

3

-4

y = 3x+1

0

3

-4

x

y

2

-2

0

-5

1

7

y = 2x

y = x - 3

x

y

x

y

8

0

4

0

3

-4

-3

1

5

0

6

-8

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- Key Points
- Make a table
- Calculate and plot 3 coordinates
- 3. Draw a line through points

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Int 2

Now try Exercise 1

Odd numbers

MIA (page 33)

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Q1. Write this number in full to 1 sig. figs

Q2. Calculate the volume of the triangular prism.

20cm

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12cm

8cm

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Learning Intention

Success Criteria

- To explain how to calculate the gradient using right angled triangles

- Gradient is :
- change in vertical height divided by
- change in horizontal distance

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- 2. Calculate simple gradients.

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Change in horizontal distance

Difference in

y -coordinates

Int 2

The gradient is the measure of steepness of a line

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Difference in

x -coordinates

The steeper a line the bigger the gradient

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m = V =

H

3

4

3

m = V =

H

2

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3

m = V =

H

5

2

m = V =

H

6

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Int 2

Round the class

Exercise 2

MIA (page 36)

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Learning Intention

Success Criteria

- To explain positive and negative gradients using coordinates.

- Know gradient formula.

- 2. Calculate gradients given two coordinates.

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The gradient using coordinates

Int 2

m = gradient

y-axis

m = Y2 – Y1

X2 – X1

y2

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y1

x-axis

O

x1

x2

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The gradient using coordinates

Int 2

Find the gradient of the line.

m = gradient

y-axis

m = Y2 – Y1

X2 – X1

m = 10 – 4

5 – 2

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m = 6 = 2

3

x-axis

O

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The gradient using coordinates

Int 2

Find the gradient of the two lines.

y-axis

m = Y2 – Y1

X2 – X1

m = Y2 – Y1

X2 – X1

m = 8 - 2

3 - 1

m = 8 – 2

-3 – (-1)

m = 6 = -3

-2

m = 6 = 3

2

x-axis

O

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The gradient using coordinates

Int 2

The gradient formula is :

(y2 – y1)

(x2 – x1)

Gradient = m =

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It is a measure of how steep a line is

A line sloping up from left to right is a positive gradient

A line sloping down from left to right is a negative gradient

Created by Mr.Lafferty Maths Dept

The gradient using coordinates

Int 2

Exercise 3

Q1 – Q3

MIA (page 37)

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Q1. Write out in full to 2 sig. figs.

Q2. A superstore make 20% profit on each can of

soup they sell. If they buy in a can for 50p.

What is the selling price.

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Q3. A hemisphere has a diameter of 10cm.

Calculate its volume.

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Learning Intention

Success Criteria

- To explain the connection between the straight line equation and the gradient.

- Understand the term standard form.

- 2. Identify the gradient m from the standard form.

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Created by Mr.Lafferty Maths Dept

10

9

8

7

6

5

4

3

2

1

x

0

-10

1

2

3

4

5

6

7

9

10

-9

-8

-6

-4

-3

-2

8

-7

-5

-1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Straight line equation and the gradient connection

y = -x - 5

y = 2x + 1

x

y

3

0

1

x

y

0

1

3

-5

-6

-8

1

3

7

m = -1

m = 2

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S4 Credit

All straight lines have the equation of the form

y = mx + c

Let’s investigate properties

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(You need GeoGebra to run link)

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y

10

All straight lines have

the equation of the form

lines are parallel if they have the same gradient

9

8

y = mx + c

7

6

5

4

3

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Where line

meets y-axis

2

Gradient

1

x

0

10

1

2

3

4

5

6

7

8

9

Find the equations of the following lines

y = -0.5x+2

y = x

y = x+4

y = 4x+2

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Int 2

Now try Exercise 3

Q4 – Q9

MIA (page 38)

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Q1. Write out in full to 1 significant fig.

Q2. A computer store buys in a laptop for £500.

They want to make a 40% profit.

How much do they sell it for.

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Q3. A line is parallel to y = 2x.

Write down its equation

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lines are parallel if same gradient

Straight Line Equation

All straight lines have the equation of the form

Slope left to right upwards positive gradient

y = mx + c

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y - intercept

Gradient

y intercept is were line cuts y axis

Slope left to right downwards negative gradient

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Int 2

Now try Exercise 4

MIA (page 41 )

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Q1. The points ( 1, 4) and (3, 11) lie on a line.

Find the gradient of the line.

Q2. Complete the table given : y = 3x+1

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Q3. Are the two lines parallel. Explain answer

y = x + 2 and y = 2x + 2

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Learning Intention

Success Criteria

- To show how to rearrange straight line equations into standard form and then identify the gradient and the
- y - intercept.

- Be able to rearrange straight line equations.
- y = mx + c

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- Identify the gradient m and y – intercept c from the standard form.
- y = mx + c

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This is called the standard form

Straight Line Equation

All straight lines have an equation of the form

y = mx + c

Where line

meets y-axis

Gradient

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If two lines have the same gradient they are parallel.

y = 2x

y = 2x+4

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Straight Line Equation

Rearrange the following straight line equations into standard form and identify the gradient and y-intercept.

Standard form

m

c

y – 3x = 4

y = 3x + 4

3

4

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2y – 2x = 6

y = x + 3

1

3

y – x + 5 = 0

y = x - 5

1

-5

4y – 8 = 0

y = 2

0

2

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Find the a line parallel to y – x = 0 and passing through (0,3).

Standard form

m

c

x – y = 0

y = x

1

0

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A line parallel to y = x has same gradient therefore m = 1

Since it passes through (0,3) then c = 3

Using standard form line is y = x + 3

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Int 2

Now try Ex 5

MIA (page 45)

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