the slope intercept equation of the line is

y = mx + b,

where m is the slope, b is the y-intercept

the line is parallel to 6x - 4y = 4

lets write 6x - 4y = 4 in slope intercept form

4y = 6x - 4 divide both sides by 4

y = (3/2)x - 1

the slope of this line is 3/2

since parallel lines have equal slopes follows m = 3/2

y = (3/2)x + b

the line goes trough (3, -1) that is for x = 3, y = -1

-1 = (3/2)*3 + b

b + 9/2 = -1

b = -1 - 9/2

b = - 11/5

the slope-intercept equation of the line is

y = (3/2)x - 11/5