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Int 2. Straight Line Graphs. Drawing Straight line graphs. The gradient. The gradient from coordinates. www.mathsrevision.com. The y intercept y = mx + c. Other forms / rearranging equation. Int 2. Q1. A house is valued at £50 000.

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straight line graphs

Int 2

Straight Line Graphs

Drawing Straight line graphs

The gradient

The gradient from coordinates

www.mathsrevision.com

The y intercept y = mx + c

Other forms / rearranging equation

Created by Mr.Lafferty Maths Dept

starter questions

Int 2

Q1. A house is valued at £50 000.

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

Starter Questions

Q2. Calculate 3.36 x 70 to 2 significant figures.

www.mathsrevision.com

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

and height 100 cm.

Created by Mr.Lafferty Maths Dept

straight line graphs3

Int 2

Straight Line Graphs

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

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

slide4

y

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

Created by Mr. Lafferty Maths Dept

straight line graphs5

Int 2

Straight Line Graphs

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

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

slide6

Straight Line Graphs

Int 2

Now try Exercise 1

Odd numbers

MIA (page 33)

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

starter questions7

Int 2

Starter Questions

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

Q2. Calculate the volume of the triangular prism.

20cm

www.mathsrevision.com

12cm

8cm

Created by Mr.Lafferty Maths Dept

the gradient of a line

Int 2

The Gradient of a Line

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

www.mathsrevision.com

  • 2. Calculate simple gradients.

Created by Mr.Lafferty Maths Dept

the gradient

Change in vertical height

Change in horizontal distance

Difference in

y -coordinates

Int 2

The Gradient

The gradient is the measure of steepness of a line

www.mathsrevision.com

Difference in

x -coordinates

The steeper a line the bigger the gradient

Created by Mr.Lafferty Maths Dept

the gradient10

Int 2

m = V =

H

3

The Gradient

4

3

m = V =

H

2

www.mathsrevision.com

3

m = V =

H

5

2

m = V =

H

6

Created by Mr.Lafferty Maths Dept

slide11

The Gradient

Int 2

Round the class

Exercise 2

MIA (page 36)

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

the gradient of a line12

Int 2

The Gradient of a Line

Learning Intention

Success Criteria

  • To explain positive and negative gradients using coordinates.
  • Know gradient formula.
  • 2. Calculate gradients given two coordinates.

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

slide13

The gradient using coordinates

Int 2

m = gradient

y-axis

m = Y2 – Y1

X2 – X1

y2

www.mathsrevision.com

y1

x-axis

O

x1

x2

www.mathsrevision.com

slide14

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

www.mathsrevision.com

m = 6 = 2

3

x-axis

O

www.mathsrevision.com

slide15

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

www.mathsrevision.com

slide16

The gradient using coordinates

Int 2

The gradient formula is :

(y2 – y1)

(x2 – x1)

Gradient = m =

www.mathsrevision.com

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

slide17

The gradient using coordinates

Int 2

Exercise 3

Q1 – Q3

MIA (page 37)

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

starter questions18

Int 2

Starter Questions

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.

www.mathsrevision.com

Q3. A hemisphere has a diameter of 10cm.

Calculate its volume.

Created by Mr.Lafferty Maths Dept

the gradient of a line19

Int 2

The Gradient of a Line

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.

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

slide20

y

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

Created by Mr. Lafferty Maths Dept

slide21

Straight Line Equation

S4 Credit

All straight lines have the equation of the form

y = mx + c

Let’s investigate properties

www.mathsrevision.com

(You need GeoGebra to run link)

Created by Mr.Lafferty Maths Dept

slide22

Straight Line Equation

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

www.mathsrevision.com

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

Created by Mr.Lafferty Maths Dept

slide23

The Gradient of a Line

Int 2

Now try Exercise 3

Q4 – Q9

MIA (page 38)

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

starter questions24

Int 2

Starter Questions

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

Created by Mr.Lafferty Maths Dept

slide25

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

www.mathsrevision.com

y - intercept

Gradient

y intercept is were line cuts y axis

Slope left to right downwards negative gradient

Created by Mr.Lafferty Maths Dept

slide26

Straight Line Graphs

Int 2

Now try Exercise 4

MIA (page 41 )

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

starter questions27

Int 2

Starter Questions

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

www.mathsrevision.com

Q3. Are the two lines parallel. Explain answer

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

Created by Mr.Lafferty Maths Dept

straight line equation

Int 2

Straight Line Equation

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

www.mathsrevision.com

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

Created by Mr.Lafferty Maths Dept

slide29

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

www.mathsrevision.com

If two lines have the same gradient they are parallel.

y = 2x

y = 2x+4

Created by Mr.Lafferty Maths Dept

slide30

Just a bit of algebra

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

www.mathsrevision.com

2y – 2x = 6

y = x + 3

1

3

y – x + 5 = 0

y = x - 5

1

-5

4y – 8 = 0

y = 2

0

2

Created by Mr.Lafferty Maths Dept

slide31

Straight Line Equation

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

www.mathsrevision.com

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

Created by Mr.Lafferty Maths Dept

slide32

Straight Line Equation

Int 2

Now try Ex 5

MIA (page 45)

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept