Rearrange 5x + 2y = 7 as 2y = 7 − 5x or y = 3.5 − 2.5x or y = -2.5x + 3.5.
Rearrange 5x + 2y = 3 as 2y = 3 − 5x or y = 1.5 − 2.5x or y = -2.5x + 1.5.
By the slope-intercept form for the equation of a line (y = mx + b), both
y = -2.5x + 3.5 and y = -2.5x + 1.5 have the same slope m equal to -2.5.
The two lines are then parallel.
Note that the two lines would be perpendicular if their slopes had a product of -1.
(For a line with a slope of -2.5, its perpendicular would then have a slope
of (-1/-2.5) or 0.4.
