Answer
$y=3x-1$
Work Step by Step
Target: $y=mx+b,$ (find m and b).
Slope: Our line has the same slope as the given line since they are parallel.
Rewrite the given line in slope-intercept form.
$6x-2y=11\qquad/-6x$
$-2y=-6y+11\qquad/\div(-2)$
$y=3x-\displaystyle \frac{11}{2}$
the slope we are after is $m=3$
Intercept:
The form of our linear equation is $y=3x+b$
To find b, substitute the coordinates of the given point and solve for b.
$0=3(\displaystyle \frac{1}{3})+b$
$0=1+b\qquad/-1$
$-1=b$
Thus,
$y=3x-1$
