The lines y = x + 4 and y = x have been graphed on the same set of axes.
Is the line y = x + 4 increasing or decreasing?
Is it steeper, flatter or equally steep as y = x?
Consider the graph of y = x - 3.
State the coordinates of the x-intercept in the form \left(x, y\right).
State the coordinates of the y-intercept in the form \left(x, y\right).
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).
State the equation of the translated line.
Consider the graph of y = 2 - x.
State the coordinates of the x-intercept in the form \left(x, y\right).
State the coordinates of the y-intercept in the form \left(x, y\right).
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).
State the equation of the translated line.
Consider the graph of y = x.
If this graph is translated 2 units down:
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = - x.
If this graph is translated 4 units down:
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of the lines y = x + 5, y = x + 2 and y = x - 3.
State whether the following statements are True or False:
They are all the same steepness.
All lines that are parallel to y = x have positive y-intercepts.
They can all be made to overlap \\y = x through a vertical translation.
They are all parallel to one another.
What do you notice about the x and y intercepts of lines that are parallel to y = x?
If a straight line is parallel to y = x and has a y-intercept of - 8, what would be its equation?
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:
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = x.
If the line was made 3 times as steep:
Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
The lines y = \dfrac{1}{2} x and y = x have been graphed on the same set of axes.
Is the line y = \dfrac{1}{2} x increasing or decreasing?
Is it steeper, flatter or equally steep as y = x?
Describe how the graph of y = x could be transformed into the graph of \\y = \dfrac{1}{2} x.
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.
The lines y = - 2 x and y = - x have been graphed on the same set of axes.
Is the line y = - 2 x increasing or decreasing?
Is the line y = - 2 x steeper, flatter or equally steep as y = - x?
Describe a transformation that would turn the graph of y = x into the graph of y = - 2 x.
Consider the graph of y = x.
If the line was rotated 90 \degree clockwise about the origin:
Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = x.
If the line was rotated 90\degree counterclockwise about the origin:
Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = 2x.
If the line was rotated 90\degree clockwise about the origin:
Where would the point \left(1, 2\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = 3x.
If the line was rotated 90\degree counterclockwise about the origin:
Where would the point \left(1, 3\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = x.
If the line was reflected about the y-axis:
Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = x.
If the line was reflected about the x-axis:
Where would the point \left(1, 1\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = -x.
If the line was reflected about the y-axis:
Where would the point \left(1, -1\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = -x.
If the line was reflected about the x-axis:
Where would the point \left(1, -1\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = 2x.
If the line was reflected about the y-axis:
Where would the point \left(1, 2\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.
Consider the graph of y = -4x.
If the line was reflected about the x-axis:
Where would the point \left(-1, 4\right) move to? State the new coordinates of the point in the form \left(x, y\right).
Sketch the graph of the new line.
State the equation of the new line.