Question

If the graph of y = -x is translated horizontally 8 units to the right and translated vertically 6 units upwards, what is its new equation?

A) y = -(x - 8) + 6
B) y = -x - 8 + 6
C) y = -(x + 8) + 6
D) y = -x + 8 + 6

Answer 1

The correct new equation after translating y = -x horizontally 8 units to the right and vertically 6 units upwards is y = -(x - 8) + 6, which reflects the horizontal and vertical shifts.

Step-by-step explanation:

When translating the graph of y = -x horizontally 8 units to the right and vertically 6 units upwards, we apply transformations to the equation. A horizontal shift to the right by 8 units is represented by replacing x with (x - 8) in the equation, and translating vertically upwards by 6 units is represented by adding 6 to the entire equation.Therefore, the new equation after both transformations is y = -(x - 8) + 6, which means option A) y = -(x - 8) + 6 is the correct answer.This new equation maintains the original slope of the line, which is negative, as well as incorporates the horizontal and vertical shifts described.