#### Answer

y=$\frac{4}{3}$x+$\frac{1}{3}$

#### Work Step by Step

To write the given equation in slope-intercept form, one must refer to the general form: y=mx+b; where m defines the slope, and b is the y-intercept. In order to convert to slope-intercept form, begin by isolating 'y'.
1. -4x+3y=1 : original equation
2. Add 4x to each side : 3y=4x+1
3. Isolate y by dividing each side by 3 : y=$\frac{4}{3}$x+$\frac{1}{3}$.