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Equations of straight lines

Objective To be able to find the equation of

straight lines.

Coordinates

Naming horizontal and vertical lines

X 3

y -2

Thursday 24th February Equations of straight

lines.

Objective to be able to give the equation of any

straight line.

Page 188, Question 3. Write down the equation of

each line on the grid. You do not need to copy

out the grid.

You have exactly 5 minutes to complete all 8

Solutions

- (e) y 6
- (f) y 4
- (g) y -3
- (h) y -5

- (a) x -9
- (b) x -5
- (c) x 4
- (d) x 8

Naming sloping lines

These points are on a straight line.

They have coordinates (-5,0), (-3,2) and (-1,4)

To find the equation of the line, find a rule

connecting the x-coordinate and the y-coordinate.

(-5 , 0) (-3 , 2) (-1 , 4)

5

5

5

The rule to find the y-coordinate is add 5 to

the x-coordinate

The equation of the line is y x 5

The equation of the line is x y 4

Coordinates (0 , 4) (1 , 3) (3 , 1)

0 4 4

1 3 4

3 1 4

The rule is x-coordinate plus y-coordinate

equals 4

Writing equations

Copy the following rules and re-write them as

equations

Rule Equation

Add 5 to the x-coordinate to get the y coordinate.

x-coordinate minus 3 equals y-coordinate.

x-coordinate plus y-coordinate equals 7

Multiply x-coordinate by 3 and subtract 4 to get the y-coordinate.

y x 5

y x - 3

x y 7

y 3x - 4

Page 190, Exercise 12E. Questions 1 2

Find the equations of the lines on the grids. You

do not need to copy out the grids.

What is the equation of the line through F and

G? A and B?

x y 15 is the equation of the line through

which points?

The octagon has 4 lines of symmetry. What are

their equations?

Friday 25th February

- Objective
- To be able to find the equations of sloping lines

- To be able to draw sloping lines from their

equations.

y x2

y x

y -x

y x -2

y 0

x 2

x 0

Sloping lines with different gradients.

Gradient is the mathematical word for

steepness. The bigger the gradient, the steeper

the slope of the line.

A line that slopes up has a positive gradient

A line that slopes down has a negative gradient.

y x

y 4x

(1, 4) (0, 0) (-1, -4)

x 4

x 4

x 4

Multiply x coordinate by 4 to get the y coordinate

y

(-2, 4) (-1, 2) (1, -2)

x -2

x -2

x -2

Equation of line y -2x

x

Multiply the x-coordinate by 2 to get the

y-coordinate

y -4x - 4

y -4x

y 2x

y 2x - 6

Monday 28th February

Objectives To be able to draw sloping lines

from their equations. To be able to find

intercepts and understand relative gradients.

y x2

x -2

y x

y -x

y x -2

y 0

y -3

x 2

x 0

x 4

You can draw sloping lines using a table of

values.

E.g. Draw the line with equation y 2x 1

1. Choose some values for x such as 3, -2, -1,

0, 1, 2, 3

2. Draw a table like this

x -3 -2 -1 0 1 2 3

y

-5

-3

-1

1

3

5

7

These are our coordinate pairs

y 2x 1

- Choose some values for x

- Draw a table for your values of x

- Work out the y values using the equation

- Plot the x and y coordinates

- Join up the points to form a straight line

- Label your line

x -3 -2 -1 0 1 2

y

-5

-3

-1

1

3

5

This grid shows the line with equation y 2x 2

The line crosses the y-axis at the point ( 0, 2 )

This point is called the intercept.

Example 1

Find the intercept of the line y 4x 5

y 4 x 0 5 y 0 5 5

y 5 3 x 0 y 5 0 5

The intercept is (0 , 5).

The intercept is ( 0 , 5 ).

What is the intercept?

y x 2

y x - 3

y 2x

y 3x 5

y 4x - 6

Gradients

Gradient is the mathematical word for steepness

The bigger the gradient, the steeper the slope of

a line.

A line that slopes up has a positive gradient

A line that slopes down has a negative gradient

Getting smaller

Getting bigger

Blue

Red

Red

Red

Blue

Which line has the biggest gradient? Red or blue?

Using graphs

Wednesday 2nd March Objective To be able to read

and interpret graphs.

What do graphs show?

A graph shows a relationship on a coordinate grid.

And across to the length axis

a) When the mass is 0kg, the spring is 10cm long

b) 19cm

c) 1.5kg

Read up from the mass axis

Sam and Anna are testing a spring. This graph

shows the relationship between the length of the

spring and the mass hung on it.

- Use the graph to find
- The length of the spring with no mass on it

b) The length of the spring with a mass of 4.5kg

c) The mass needed to make the spring 13cm long.

Using a scale

Graphs often have different scales on each

axis. The most common scales are

The factors of 10 1, 2, 5, 10

The multiples of 10 10, 20, 50, 100

You work out a scale like this

50 10 5

5 10 0.5

Graphs in all 4 quadrants

You can use this graph to convert temperatures

between degrees Fahrenheit (0F) and degrees

Celsius (0C)

You need to be able to use graphs in all four

quadrants.

Use the graph to convert 500C into 0F

Read down from 500C

The answer is 600F

And across to the vertical axis

300C

-100F

00C

1000F

-260C

400F

-700C

-550F

1600F

600C

What can you tell me about

The blue line?

Compared to the red line?

The yellow line?

The green line?

Compared to the yellow line?

The pink line?