Question

Are the equations y-6x=-2 and y=6x-2 representing the same line or different lines?

Answer 1

To determine if the equations \( y - 6x = -2 \) and \( y = 6x - 2 \) represent the same line, we can rewrite both equations in slope-intercept form (which has the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept).

1. The first equation is \( y - 6x = -2 \).
We can rearrange it to solve for \( y \):
\[
y = 6x - 2
\]

2. The second equation is already in slope-intercept form: \( y = 6x - 2 \).

Since both equations simplify to \( y = 6x - 2 \), they represent the same line. Thus, the answer is that the equations represent the same line.