Question

task 8
graph & label line a: \\( y = 2x + 6 \\)
graph & label line b: reflected across
the y - axis and
translated down 6
coordinate grid image
write the equation of line b:

Explanation:

Step1: Reflect across y - axis

To reflect a function \( y = f(x) \) across the \( y \) - axis, we replace \( x \) with \( -x \). For the line \( y = 2x+6 \), after reflecting across the \( y \) - axis, the equation becomes \( y = 2(-x)+6=- 2x + 6 \).

Step2: Translate down 6 units

To translate a function \( y = f(x) \) down by \( k \) units, we subtract \( k \) from the function. Here, \( k = 6 \). So we take the equation from Step 1 (\( y=-2x + 6 \)) and subtract 6 from it.
\( y=-2x+6 - 6=-2x \)

Answer:

The equation of line B is \( y=-2x \)