Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 40
Chapter 7: Graphs
Drawing Straight line Graphs from the Equation
Look at Carla’s table of values for y = 2x – 4.
x
0
1
2
3
4
2x
0
2
4
6
8
–4
–4
–4
–4
–4
–4
y
–4
–2
0
2
4
2x is twice x
-4 stays the
same whatever
the value of x
These are the values of y = 2x – 4
5
Carla draws the graph.
The steepness of a line is called its gradient.
4
y = 2x - 4
3
2
In the case of y = 2x – 4, when x increases
by 4 then y increases by 8 so
y-axis
1
-2
0
-1
0
1
2
3
4
-1
-2
-3
?
When x increases by 3, what does y increase
by?
Do these values still give a gradient of 2?
-4
-5
x-axis
What can you say about the gradients of parallel lines?
?
Is y = 2x + 1 parallel to y = 2x – 4?
7 Graphs
In this graph the scales for x and
y are the same. You can have
different scales on the two axes.
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5
Name of Lecturer: Mr. J.Agius
1
Course: HVAC1
Draw a grid from -8 to 8 on both axes.
Draw the graph of each of the following lines. Don’t forget to label them. (Note: Not all x
values will produce a y value that you can plot within the range given. If you are
unsuccessful with one x value then think carefully before trying another.)
a) y = x + 4
b)
y = 2x
c) y = 4 – x
d) y = 3x – 8
e)
x=7
f)
y=5
Write down the co-ordinates of the point where
g) y = x + 4 meets y = 2x
h) y = 4 – x meets y = 3x – 8
i)
2
y = x + 4 meets y = 4 – x
On a graph paper provided, plot the graph of y = 4x + 2 in the range -1 ≤ x ≤ 4, using a
scale of 2cm to represent one unit on the x-axis and 2cm to represent one unit on the yaxis.
x
-1
0
1
2
3
4
4x
2
+2
y
-2
18
From your graph:
i)
Calculate the gradient of the line (show necessary lines on plot)
ii)
Determine the y-intercept.
iii) State the value of x when the graph has a value of 5.
iv) For which value of y is x = 1.5?
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Name of Lecturer: Mr. J.Agius
3
Course: HVAC1
On a graph paper provided, plot the graph of y = -2x + 4 in the range -1 ≤ x ≤ 4, using a
scale of 2cm to represent one unit on the x-axis and 2cm to represent one unit on the yaxis
x
-2x
+4
y
-1
0
1
2
3
4
+4
6
-4
From your graph:
i)
Calculate the gradient of the line (show necessary lines on plot)
ii)
Determine the y-intercept.
iii) State the value of x when the graph has a value of 5.
iv) For which value of y is x = 1.5?
4
This function machine doubles the input x and then adds three, to obtain output y.
Input
×2
x
a) Fill in:
Output
+3
y
When x = 0, y = ________
When x = 1, y = ________
When x = ________, y = 9
When x = ________, y = 11
b) Copy your answer in the form of co-ordinates:
(0, ___ ), (1, ___ ), ( ___, 9), ( ___, 11)
Now plot the four points that have these co-ordinates and then join them.
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Name of Lecturer: Mr. J.Agius
Course: HVAC1
12
11
10
9
8
7
6
5
4
3
2
1
0
-1 0
1
2
3
4
5
6
7
8
-2
-3
-4
-5
5
The following table gives the force F newtons which, when applied to a lifting machine,
overcomes a corresponding load of L newtons.
F newtons
19
35
50
93
125
147
L newtons
40
120
230
410
540
680
Choose suitable scales and plot a graph with F representing the vertical axis and L
a)
the horizontal axis. Label the graph and its axes.
b) Find the slope of the graph.
c) From the graph determine
i)
the force applied when the load is 325 N, and
ii) the load that a force of 45N will overcome.
d)
If the graph were to continue in the same manner what value of force would be
needed to overcome a 750N load?
e) State the equation of the graph.
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