When the lines are given in standard form (Ax+By+C), they are ideal for checking parallelism and perpendicularity because if there is a vertical line, the y term will simply disappear, i.e. B=0, while in the slope-intercept form, the slope m will become infinity, which is not the case here.
For checking parallelism, try to multiply or divide to equalise one of the two coefficients, A, or B, and compare the other one. C will be different for parallel lines.
3x-10y+15 = 0, and
30x-10y+24 = 0
We see that B is equal while A is different, we conclude that the two lines are not parallel.
thank you! :)