The Family of Linear Functions Has a Parent Function Y=X

Name: ______

Inquiry Lab

Families of Linear Graphs

Go to www.desmos.com and launch calculator

The family of linear functions has a parent function y=x.

On Desmos, type in y=x

1.) Sketch it here

2.) Identify m ______

3.) Identify b ______

On Desmos, type in y= 2x

4.) How did the line change with respect to y=x?

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On Desmos, type in y= 1 2x

5.) How did the line change with respect to y=x?

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On Desmos, type in y = -x

6.) How did the line change with respect to y=x?

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On Desmos, clear: y= 12x, y=-x (Keep y = x and y = 2x)

On Desmos type in: y = 2x +6

7.) Compare the lines y = 2x and y=2x +6. What are their similarities and differences?

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8.) Which two lines are parallel? (Parallel lines will never cross)

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9.)What do the equations of parallel lines have in common?

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On Desmos, type in y= 2x-2

10.) What do the lines y=2x, y=2x+6, and y=2x-2 all have in common?

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11.)Name three parallel lines displayed on your Desmos?

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12.) What do the lines y=2x, y=2x +6 and y=2x -2 all have that are different?

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Clear all lines on Desmos, except for the model graph of y=x

On Desmos, type in y=-13 x +1 and y=3x -4

13.) Compare the graphs of y=-13x +1 and y=3x -4?

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14.) Do the graphs of y=-13x +1 and y=3x -4 cross? Does it look like they cross at a 90 degree angle?

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15.) Are the slopes of the graphs y=-13x +1 and y=3x -4 the opposite reciprocals of each other?

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16.)If the definition of perpendicular lines is that the slopes are the opposite reciprocals of each other and the graphs cross at a 90 degree angel are the graphs of y=-13x +1 and y=3x -4 perpendicular?

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Clear all graphs on Desmos

17.) How does changing the slope or y-intercept affect the graph of a linear function?