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Equations of straight lines

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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 Thursday 24th February ... – PowerPoint PPT presentation

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Title: Equations of straight lines


1
Equations of straight lines
Objective To be able to find the equation of
straight lines.
2
Coordinates












3
Naming horizontal and vertical lines
X 3












y -2
4
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
5
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

6
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
7












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
8
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
9
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.
10
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?
11
Friday 25th February
  • Objective
  • To be able to find the equations of sloping lines
  • To be able to draw sloping lines from their
    equations.

12
y x2
y x
y -x










y x -2
y 0
x 2
x 0
13
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.
14
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
15
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
16
y -4x - 4
y -4x
y 2x












y 2x - 6
17
Monday 28th February
Objectives To be able to draw sloping lines
from their equations. To be able to find
intercepts and understand relative gradients.
18
y x2
x -2
y x
y -x










y x -2
y 0
y -3
x 2
x 0
x 4
19
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
20
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
21
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.
22
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 ).
23












What is the intercept?
y x 2
y x - 3
y 2x
y 3x 5
y 4x - 6
24
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
25
Getting smaller
Getting bigger






Blue
Red
Red
Red
Blue
Which line has the biggest gradient? Red or blue?
26
Using graphs
Wednesday 2nd March Objective To be able to read
and interpret graphs.
27
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.
28
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
29
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
30
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?
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