Question

"Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x - 8?

A) It is the graph of y = x translated 8 units down.
B) It is the graph of y = x where the slope is decreased by 8.
C) It is the graph of y = x translated 8 units to the left.
D) It is the graph of y = x translated 8 units up."

Answer 1

The graph of y = x - 8 is the graph of y = x translated 8 units down. This changes the y-intercept but the slope remains the same, so the graph is still a straight line with a positive slope.

Step-by-step explanation:

The graph of y = x - 8 is a transformation of the graph of y = x. The correct description of this transformation is that it translates the graph of y = x 8 units down. This is because the -8 is subtracted from the y-value of every point on the graph of y = x, effectively moving the entire line down 8 units on the y-axis. The slope of the graph remains unchanged; it is still a straight line with positive slope. Figure A1 Slope and the Algebra of Straight Lines mentions the importance of the slope and y-intercept in defining the shape of a straight line. In this case, the subtraction of 8 affects the y-intercept but does not alter the slope.