Question 93842
"L passes through (5,6) and is perpendicular to 3x-5y=15"



First convert  3x-5y=15 into slope intercept form


*[invoke converting_linear_equations "standard_to_slope-intercept", 3, -5, 15, 2, 1]


Now lets find the perpendicular line 


*[invoke equation_parallel_or_perpendicular "perpendicular", "3/5", -3, 5, 6]



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"L has y-intercept(0,-3) and is paralell to -3x+5y=-15"


First convert -3x+5y=-15 into slope intercept form


*[invoke converting_linear_equations "standard_to_slope-intercept", -3, 5, -15, 2, 1]


Now lets find the parallel line 


*[invoke equation_parallel_or_perpendicular "parallel", "3/5", -3, 0, -3]


So the equation parallel to {{{-3x+5y=-15}}} and that goes through (0,-3) is {{{(3/5)x-3}}} (or {{{-3x+5y=-15}}})