Copy of Linear Relations Transformations
Linear Relations Transformations
Linear Relation Transformation Exercise
The linear Relation y = x, denoted by line g.
The slope-intercept form isy = mx + b, where m=slope and b=y-intercept of the relation.
Note: The 'slider' feature on the x-y coordinate plane can be used to change the m and b along with a new parameter c for the following exercises. To do so, place the cursor and hold it on the dot of the slider and slide it to the desired m and b values. To move the slider to a different location on the x-y plane, place the cursor and hold it on the line of the slider and move it to the desired location.
Note: You can zoom in or out with the mouse.
Exercise 1
Perform the following linear relation transformation:
Vertical shift of 3 units up (y-intercept = 3).
The new relation is y=x +3 , denoted by line f.
Set the slope of the relation to m=1 by entering 1 for m.
Set the y-intercept of the relation to b=3 by entering 3 for b.
Set the x-intercept of the relation to c=0 by entering 0 for c.
Observe the transformation of the linear relation.
Exercise 2
Perform the following linear relation transformation:
Vertical shift of 3 units down (y-intercept = -3).
The new relation is y=x - 3 , denoted by line f.
Set the slope of the relation to m=1 by entering 1 for m.
Set the y-intercept of the relation to b=-3 by entering -3 for b.
Set the x-intercept of the relation to c=0 by entering 0 for c.
Observe the transformation of the linear relation.
When you change the y-intercept how does the graph change?
Exercise 3
Perform the following linear relation transformation:
Vertical stretch of the linear relation to 2.
The new relation is y=2x , denoted by line f.
Set the slope of the relation to 2 by entering 2 for m.
Set the y-intercept of the relation to b=0 by entering 0 for b.
Set the x-intercept of the relation to c=0 by entering 0 for c.
Observe the transformation of the linear relation.
When you make the slope greater than 1 how does the graph change?
Exercise 4
Perform the following linear relation transformation:
Vertical compression of the linear relation to 0.5.
The new relation is y=0.5x , denoted by line f.
Set the slope of the relation to 0.5 by entering 0.5 for m.
Set the y-intercept of the relation to b=0 by entering 0 for b.
Set the x-intercept of the relation to c=0 by entering 0 for c.
Observe the transformation of the linear relation.
When you make the slope between 0 and 1 how does the graph change?
Exercise 5
Perform the following linear relation transformation:
Vertical stretch and REFLECTION of the linear relation to - 1.
The new relation is y= - 1x ,denoted by line f.
Set the slope of the relation to -1 by entering -1 for m.
Set the y-intercept of the relation to b=0 by entering 0 for b.
Set the x-intercept of the relation to c=0 by entering 0 for c.
Observe the transformation of the linear relation.
When you make the slope a negative integer how does the graph change?
Exercise 6
Perform the following linear relation transformation:
Horizontal shift of the linear relation by 4
The new relation is y= (x+4) , denoted by line f.
Set the slope of the relation to 0 by entering zero for m.
Set the y-intercept of the relation to b=0 by entering 0 for b.
Set the x-intercept of the relation to 4 by entering 4 for c.
Observe the transformation of the linear relation.
Exercise 7
Perform the following linear relation transformation:
Horizontal shift of the linear relation by -4
The new relation is y= (x-4) , denoted by line f.
Set the slope of the relation to 0 by entering zero for m.
Set the y-intercept of the relation to b=0 by entering 0 for b.
Set the x-intercept of the relation to 4 by entering 4 for c.
Observe the transformation of the linear relation.
When you make change c how does the graph change?
Putting it all together
Perform the following linear relation transformation:
The new relation is y= -1(x-4)+3 , denoted by line f.
Describe all the transformations to the line y=x