The given equation is of the form y = mx + b, where m is the slope and b is the y-intercept.
So in the equation y = 3x - 2, the slope is 3.
And we know that perpendicular lines have opposite reciprocal slopes. So the slope of the line you want is:
[tex]m=\frac{-1}{3}=-\frac{1}{3}[/tex]
Next, we have the point (6,8). So, Use the slope-intercept form of a line to substitute those values and write your new equation:
[tex]\begin{gathered} y=mx+b \\ 8=(-\frac{1}{3})(6)+b \\ 8=-2+b \\ 8+2=-2+b+2 \\ b=10 \end{gathered}[/tex]
The new equation is:
[tex]y=-\frac{1}{3}x+10[/tex]
Answer: B.
