You can put this solution on YOUR website! The easiest way, is to convert into slope-interecept (y=mx+b) form.
-10x + 6y = -30; add 10 x to both sides
6y = 10x - 30; now, divide both sides by 6, and reduce fraction
y = 5/3x - 5
Therefore, the slope is , and for the record, the y-intercept is -5.
You can put this solution on YOUR website! Actually the easiest way since it is in standard form is to use -a/b for the slope
-a/b
-(-10/6)=5/3
the y intercept is when x=0 and here y=-5 (0,-5)
the x intercept when y=0 is x=3 (3,0)