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Maths Quest Maths B Year 11 for Queensland
WorkSHEET 1.2
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Chapter 1 Linear functions WorkSHEET 1.2
Linear functions
Sketch the graph with equation y = 3x – 6.
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Name: ________________________
y = 3x – 6
y-intercept: when x = 0, y = – 6
x-intercept: when y = 0, x = 2
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Sketch the graph with equation
2y – 6x – 12 = 0 .
2y – 6x – 12 = 0
y-intercept: when x = 0, y = 6
x-intercept: when y = 0, x = –2
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Solve the following equations simultaneously:
y = 2x – 1
y = 5x + 2
What is the point of intersection of the
following two lines?
3x + 2y = –10
x + 4y = 5
y = 2x – 1
y = 5x + 2
2x – 1 = 5x + 2
–3 = 3x
x = –1 and y = – 3
Solution (–1, –3)
[1] 3x + 2y = – 10
[2] x + 4y = 5
[1]  2: 6x + 4y = –20
[3]
[3] – [2]: 5x = –25
x = –5
Substitute x = –5 into equation [1]
[1]: 3  –5 + 2y = –10
2y = 5
y = 2.5
Solution (–5, 2.5)
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Maths Quest Maths B Year 11 for Queensland
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Chapter 1 Linear functions WorkSHEET 1.2
Sixty students on ‘The Great Bike Ride’
consume either three meals a day or four meals
a day. If 213 meals are consumed on one
particular day, how many students ate four
meals?
What is the gradient of the line which is
parallel to the line with equation:
3y  2x  6 ?
Let t = students having three meals in a day
and f = students having four meals in a day
[1] t + f = 60
[2] 3t + 4f = 213
[1]  3: 3t + 3f = 180 [3]
[2] – [3]: f = 33
33 students have four meals on that day.
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.
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A parallel line will have the same gradient.
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Therefore the gradient of the line is .
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What is the gradient of the line which is
parallel to the line which connects the two
points (–3, 5) and (2, –7)?
What is the equation of the line with gradient
–3 and passing through the point (–2, –5)?
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3y  2x  6
3y  2x  6
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y  x6
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The gradient of this line is
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The two points are (–3, 5) and (2, –7).
y  y1
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75
Gradient = 2
=
=

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x 2  x1
2 3
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Gradient of parallel line is  .
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Equation of line is found using:
y  y1  m( x  x1 )
Substituting values, y   5  3( x  2)
y  5  3( x  2)
y  5  3x  6
0  3x  y  11
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Maths Quest Maths B Year 11 for Queensland
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Chapter 1 Linear functions WorkSHEET 1.2
What is the equation of the line which passes
through the points (–1, 0) and (3, –2)?
What is the equation of the line which passes
through the point of intersection of the lines
with equations
2x + y – 1 = 0
and
3x – y + 6 = 0
and is parallel to the line with equation
7x – 4y – 1 = 0?
The two points are (–1, 0) and (3, –2).
y  y1
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20
Gradient = 2
=
=  =

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x 2  x1
3 1
Equation of line is found using:
y  y1  m( x  x1 )
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Substitute (1, 0) and m   :
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y  0   ( x   1)
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2 y  ( x  1)
2 y  x 1
x  2 y 1  0
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[1] 2x + y = 1
[2] 3x – y = –6
[1] + [2]: 5x = –5
x = –1
Substitute x = –1 into equation [1])
[1]: 2  –1 + y = 1
y=3
Point of intersection: (–1, 3)
[3] 7x – 4y – 1 = 0
7x – 1 = 4y
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y  x
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Gradient of this line is .
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Gradient of parallel line is .
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Equation of the line is found using:
y  y1  m( x  x1 ) .
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Substitute (1, 3) and m  :
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y  3  ( x   1)
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4 y  12  7( x  1)
4 y  12  7 x  7
7 x  4 y  19  0
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