Comparing Linear Functions to y=x

Mr. Bowman explains how to compare linear functions to the parent function y = x. He first analyzes the function y = 1/5x, discussing its slope and y-intercept compared to y = x, concluding that it is less steep with no vertical shift. Next, he examines y = x + 3, noting that it has the same slope as y = x but a vertical shift upwards by three units.

What is the parent function of all linear functions?

• y = 2x

• y = x

• y = x + 1

• y = x^2

How does the steepness of y = (1/5)x compare to y = x?

• It is steeper

• It is not a linear function

• It is equally steep

• It is less steep

What is the slope of the function y = (1/5)x?

• 1

• 5

• 0

• 1/5

Where does y = (1/5)x cross the y-axis compared to y = x?

• It does not cross the y-axis

• At a higher point

• At the same point

• At a lower point

What is the y-intercept of y = (1/5)x?

• 0

• 1

• 1/5

• 5

How does the steepness of y = x + 3 compare to y = x?

• It is less steep

• It is not a linear function

• It is steeper

• It is equally steep

What is the slope of the function y = x + 3?

• 3

• 1

• 0

• x

Where does y = x + 3 cross the y-axis compared to y = x?

• At a lower point

• At the same point

• It does not cross the y-axis

• At a higher point

What is the y-intercept of y = x + 3?

• 0

• 1

• 3

• x

What does adding a constant to the function y = x do to its graph?

• Shifts it horizontally

• Shifts it vertically

• Makes it non-linear

• Changes its slope