08/10/20141 Linear Graphs Learning Intention: by the end of the lesson, students should be able to: ...
16
16/05/22 1 Linear Graphs Learning Intention: by the end of the lesson, students should be able to: generate coordinate pairs that satisfy a simple linear rule plot the graphs from an equation E.g.: y = 2x Success Criteria: students will know they can do this when their coordinate pairs derived from an equation produce a straight line Keywords: substitute, intercept, gradient, origin, parallel
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Transcript of 08/10/20141 Linear Graphs Learning Intention: by the end of the lesson, students should be able to: ...
11/04/23 1
Linear GraphsLearning Intention: by the end of the lesson,
students should be able to:generate coordinate pairs that satisfy a simple linear
rule plot the graphs from an equation E.g.: y = 2x
Success Criteria: students will know they can do this when their coordinate pairs derived from an equation produce a straight line
Keywords: substitute, intercept, gradient, origin,parallel
11/04/23 Presented By J. Mills-Dadson 2
Linear Graphs
Linear graphs are ______ linesstraight
• The rule connecting x and y coordinates is of the form y = mx + c
• ‘m’ is the gradient : how flat or how steep the graph should be
• ‘c’ is the intercept: where the graph crosses the y-axis
• The meeting points of the x - axis and y – axis is called the origin
11/04/23 Presented By J. Mills-Dadson 3
Linear Graphs
x 0 1 2 3
y
1) Let us start with simple rule, y = x
0 1 2 3
x 0 1 2 3
y
2) Now let’s y = x + 2
2 3 4 5
x 0 1 2 3
y
Now let’s y = 2x + 2
2 4 6 8
Let’s plot the coordinates of the
first two rules on one grid.
y
10
9
8
7
6
5
4
3
2
1
x0 432-3 -2 -1 1 5-1
-2
-3
y
10
9
8
7
6
5
4
3
2
1
x0-3 -2 -1 1 2 3 4 5-1
-2
-3
Join the points to draw the
graph
y = xy
= x +
2
What
can
you
say
abo
ut the
slop
e an
d
wher
e th
e cr
oss th
e y – a
xis?
11/04/23 Presented By J. Mills-Dadson 4
Linear Graphs
x 0 1 2 3
y
2) Now let’s y = x + 2
2 3 4 5
x 0 1 2 3
y
Now let’s y = 2x + 2
2 4 6 8
Let’s plot the coordinates of the
These two rules on one grid.
y
10
9
8
7
6
5
4
3
2
1
x0 432-3 -2 -1 1 5-1
-2
-3
y
10
9
8
7
6
5
4
3
2
1
x0-3 -2 -1 1 2 3 4 5-1
-2
-3
Join the points to draw the
graph
y = x
+ 2
What can you say about the slope and
where the cross the y – axis?
y =
x +
2
11/04/23 Presented By J. Mills-Dadson 5
What is the mathematical keyword used to describe the slope (flatness and steepness) of a linear graph?
A origin B intercept
D x-axis
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C gradient
Plenary
C gradient
11/04/23 Presented By J. Mills-Dadson 6
Linear graphs are :
A straight lines B circles
D none of the above
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C curves
Plenary
A straight lines
100,000
11/04/23 Presented By J. Mills-Dadson 7
Look at y = 3x + 1. What is the value of the gradient?
A 1 B 4
D 3
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C 2
Plenary
D 3
200,000
11/04/23 Presented By J. Mills-Dadson 8
What is the mathematical keyword used to describe where a linear graph crosses the y-axis?
A parallel B intercept
D x-axis
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C gradient
Plenary
B intercept
300,000
11/04/23 Presented By J. Mills-Dadson 9
Which pair of linear graphs have the same gradient (slope)?
A y = 2x + 1 & y = 3x + 1 B y = 3x +2 & y = 3x +3
D all of the above
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C y = x - 2 & y = 2x + 5
Plenary
B y = 3x + 2 & y = 3x +3
400,000
11/04/23 Presented By J. Mills-Dadson 10
Look at y =x + 1. When x is 3, what would y be?
A 4 B 1
2
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C 3
Plenary
A 4
500,000
11/04/23 Presented By J. Mills-Dadson 11
What is the name of the point where the x-axis and the y axis meet?
A origin B intercept
D parallel
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C slope
Plenary
A origin
600,000
11/04/23 Presented By J. Mills-Dadson 12
When linear graphs cross the y - axis at different points, we say the graphs have the different………
A origins B intercepts
D lengths
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C gradients
Plenary
B intercepts
700,000
11/04/23 Presented By J. Mills-Dadson 13
Look at y = 2x + 2. If x is 7, what would y be?
A 2 B 7
D 16
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C 14
Plenary
C 16
800,000
11/04/23 Presented By J. Mills-Dadson 14
When a linear graph slopes downwards from left to right, it means the gradient is……….
A 0 B positive
D none of the above
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C negative
Plenary
C negative
900,000
11/04/23 Presented By J. Mills-Dadson 15
Look at y = -2x – 2. If x is 10, what would y be?
A -10 B -2
D -22
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
C -18
Plenary
C -22
1,000,000
Today’s Class Work
Exercise 3A – Plotting Straight Line GraphsQ1 adgjQ2aeiQ3 allQ4 Q5
Book check:2A Linear equations2B Worded problems2C Substitution and
transposing
Redemption work:4B Correlation
coefficient4C Two mean method
11/04/23 16
