Answer
$y=\displaystyle \frac{3}{4}x-\frac{5}{4}$
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.
$3x-4y=8\qquad/-3x$
$-4y=-3y+8\qquad/\div(-4)$
$y=\displaystyle \frac{3}{4}x-2$
the slope we are after is $m=\displaystyle \frac{3}{4}$
Intercept:
The form of our linear equation is $y=\displaystyle \frac{3}{4}x+b$
To find b, substitute the coordinates of the given point and solve for b.
$-1=\displaystyle \frac{3}{4}(\frac{1}{3})+b$
$-1=\displaystyle \frac{1}{4}+b\qquad/-\frac{1}{4}$
$-\displaystyle \frac{5}{4}=b$
Thus,
$y=\displaystyle \frac{3}{4}x-\frac{5}{4}$
