If the equation of a line is modified to y = f(x) + a, which direction is the line moved?

If the equation of a line is modified to y = f(x) + a, which direction is the line moved?

• A. Left on the x axis
• B. Right on the x axis
• C. Up on the y axis
• D. Down on the y axis

Answer: (C)

When the equation of a line is expressed as \( y = f(x) + a \), the term \( a \) directly impacts the position of the line on the Cartesian plane. Specifically, the value of \( a \) represents a vertical shift of the line. If \( a \) is positive, the entire graph of the function \( f(x) \) is moved upward by \( a \) units on the y-axis. Conversely, if \( a \) were negative, the graph would shift downward. The function itself, \( f(x) \), remains unchanged in shape or direction; only its vertical position is altered. This means that the line would move in a vertical direction (upward if \( a > 0 \) and downward if \( a < 0 \)). Hence, the correct answer is that the line is moved upward on the y-axis when modified by adding a positive constant to the function.

When the equation of a line is expressed as ( y = f(x) + a ), the term ( a ) directly impacts the position of the line on the Cartesian plane. Specifically, the value of ( a ) represents a vertical shift of the line.

If ( a ) is positive, the entire graph of the function ( f(x) ) is moved upward by ( a ) units on the y-axis. Conversely, if ( a ) were negative, the graph would shift downward. The function itself, ( f(x) ), remains unchanged in shape or direction; only its vertical position is altered.

This means that the line would move in a vertical direction (upward if ( a > 0 ) and downward if ( a < 0 )). Hence, the correct answer is that the line is moved upward on the y-axis when modified by adding a positive constant to the function.