how do you find the slope of 10x-5y=270

quick way would be to know that for

Ax + By = C, the slope is -A/B

so for your equation, slope = -10/-5 = 2

or, change your equation to the form y=mx + b, then m is the slope

so...
10x-5y=270
-5y = -10x + 270, now divide both sides by -5
y = 2x - 54, so the slope is 2, as above.