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CanadaON
Grade 9

6.08 Transformations of y=x

Worksheet
Translations
1

The lines y = x + 4 and y = x have been graphed on the same set of axes.

a

Is the line y = x + 4 increasing or decreasing?

b

Is it steeper, flatter or equally steep as y = x?

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2

Consider the graph of y = x - 3.

a

State the coordinates of the x-intercept in the form \left(x, y\right).

b

State the coordinates of the y-intercept in the form \left(x, y\right).

c

If the graph is translated 6 units down, what will be the coordinates of the new y-intercept?

State the coordinates in the form \left(x,y\right).

d

State the equation of the translated line.

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3

Consider the graph of y = 2 - x.

a

State the coordinates of the x-intercept in the form \left(x, y\right).

b

State the coordinates of the y-intercept in the form \left(x, y\right).

c

If the graph is translated 10 units up, what will be the coordinates of the new y-intercept?

State the coordinates in the form \left(x, y\right).

d

State the equation of the translated line.

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4

Consider the graph of y = x.

If this graph is translated 2 units down:

a

Sketch the graph of the new line.

b

State the equation of the new line.

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5

Consider the graph of y = - x.

If this graph is translated 4 units down:

a

Sketch the graph of the new line.

b

State the equation of the new line.

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6

Consider the graph of the lines y = x + 5, y = x + 2 and y = x - 3.

a

State whether the following statements are True or False:

i

They are all the same steepness.

ii

All lines that are parallel to y = x have positive y-intercepts.

iii

They can all be made to overlap \\y = x through a vertical translation.

iv

They are all parallel to one another.

b

What do you notice about the x and y intercepts of lines that are parallel to y = x?

c

If a straight line is parallel to y = x and has a y-intercept of - 8, what would be its equation?

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Rotations and changes in steepness
7

Consider the graph of y = x, with the point \left(1, 1\right) that lies on the graph.

If the steepness of this graph is quadrupled:

a

Sketch the graph of the new line.

b

State the equation of the new line.

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8

Consider the graph of y = x.

If the line was made 3 times as steep:

a

Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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9

The lines y = \dfrac{1}{2} x and y = x have been graphed on the same set of axes.

a

Is the line y = \dfrac{1}{2} x increasing or decreasing?

b

Is it steeper, flatter or equally steep as y = x?

c

Describe how the graph of y = x could be transformed into the graph of \\y = \dfrac{1}{2} x.

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10

Consider the given graph of y = - x.

Sketch the graph of a straight line whose y value is decreasing at a faster rate than y = - x.

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11

The lines y = - 2 x and y = - x have been graphed on the same set of axes.

a

Is the line y = - 2 x increasing or decreasing?

b

Is the line y = - 2 x steeper, flatter or equally steep as y = - x?

c

Describe a transformation that would turn the graph of y = x into the graph of y = - 2 x.

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12

Consider the graph of y = x.

If the line was rotated 90 \degree clockwise about the origin:

a

Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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13

Consider the graph of y = x.

If the line was rotated 90\degree counterclockwise about the origin:

a

Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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14

Consider the graph of y = 2x.

If the line was rotated 90\degree clockwise about the origin:

a

Where would the point \left(1, 2\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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15

Consider the graph of y = 3x.

If the line was rotated 90\degree counterclockwise about the origin:

a

Where would the point \left(1, 3\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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Reflections
16

Consider the graph of y = x.

If the line was reflected about the y-axis:

a

Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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17

Consider the graph of y = x.

If the line was reflected about the x-axis:

a

Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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18

Consider the graph of y = -x.

If the line was reflected about the y-axis:

a

Where would the point \left(1, -1\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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19

Consider the graph of y = -x.

If the line was reflected about the x-axis:

a

Where would the point \left(1, -1\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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20

Consider the graph of y = 2x.

If the line was reflected about the y-axis:

a

Where would the point \left(1, 2\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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21

Consider the graph of y = -4x.

If the line was reflected about the x-axis:

a

Where would the point \left(-1, 4\right) move to? State the new coordinates of the point in the form \left(x, y\right).

b

Sketch the graph of the new line.

c

State the equation of the new line.

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Outcomes

9.C4.3

Translate, reflect, and rotate lines defined by y = ax, where a is a constant, and describe how each transformation affects the graphs and equations of the defined lines.

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