the given line is,
-5x + 3y = 1
first of all lets establish the slope of the given line
the eqaution of a line in slope-intercept form is,
y = mx + b
where m is the slope, b is the y-intercept
lets arrange the given line eqaution in the form of the slope formular above
so,
3y = 1 + 5x
3y = 5x + 1
making y the subject of formular,
y = 5x/3 + 1/3
therefore:
a) a line that is parallel with slope m = 5/3
b) the slope that is perpendicular to the given line
the perpendicular slope is the opposite reciprocal
that is, m1 . m2 = -1
recall, m1 = 3/5
m2 = -1 X 3/5
= -3/5
therefore the perpendicular slope is -3/5