Question

Write the equation of the line that passes through (0, 3) and is parallel to the line 3x + 5y = 6.

Answer 1

do you know what the slope is in 3x + 5y = 6 ? If not, do you know how to find it ?

Answer 2

In y = mx + b form, the m position is the slope
3x + 5y = 6 (put this in y = mx + b form)
5y = -3x + 6
y = -3/5x + 6/5
the slope(m) = -3/5

A parallel line will have the same slope.
now we use y = mx + b
slope(m) = -3/5
(0,3) x = 0 and y = 3
now sub
y = mx + b
3 = -3/5(0) + b
3 = b

your equation is : y = -3/5x + b...but we need it in standard form Ax + By = C
y = -3/5x + 3 -- multiply by 5 to get rid of the fraction
5y = -3x + 3 -- add 3x to both sides
3x + 5y = 3 <== your parallel line