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Graph of a linear function transformation

Question:

From the graph of y = - (3/2) x to get the graph of y = - (3x - 4)/2, which of the following statement is true?

A. move the graph of y = - (3/2) x up 4 units.

B. move the graph of y = - (3/2) x down 4 units.

C. move the graph of y = - (3/2) x up 2 units.

D. move the graph of y = - (3/2) x down 2 units.

Solution:

Given y = - (3/2) x. The question asked how do we get the graph of y = - (3x - 4)/2 by move the graph of y = - (3/2) x.

y = - (3x - 4)/2
= - (3x/2 - 4/2)
= -3x/2 + 2

Therefore, move the graph of y = - 3x/2 up 2 units, we can get the graph of y = - (3x -4)/2

how to transform the graph of a linear function to get the graph of another linear function?

Look the figure shown above, the blue line is the graph of y = - (3/2) x. It passes the origin. Because its slope is negative so, the y decrease as x increase. By move the blue line up 2 units, we het the graph of y = - (3x - 4)/2. Watch the video for more details.