Verified answer

the general equation of a line is y = m*x + b ... where m = the slope and b = the place where the line crosses the y-axis when x=0.

So to know the slope, the best way is to solve for y.

5x - 2y = 10

subtract 5x from both sides

- 2y = 10 - 5x

divide both sides by -2

y = -10/2 + (5x)/2

y = (5/2) x - 5

therefore ... the slope of the line is (5/2)

Long-winded answer (hopefully not too condescending):

So (as you probably know) the word "slope" is another way of saying "gradient"? And the gradient of a straight line is the ratio of how much y increases as x increases by 1. You can write this as (change in y) ÷ (change in x). But instead of drawing out the line to see this you can just use this clever cheat (which, again, you probably already know about) to find the gradient...

In any line with a formula like y=mx + c (with m and c being constant numbers), m is the gradient and c is where the line crosses the y axis. So if the equation was in this form you could just read it off. But the equation isn't in that form so you need to rearrange it to put it in that for. like so:

5x - 2y = 10

(add 2y to both sides)

5x = 10 +2y

(-10 from both sides)

5x - 10 = 2y

(divide both sides by 2)

2.5x - 5 = y

or, y = 2.5x - 5

so you can read off the gradient as 2.5.

Easy...!

2y = 5x - 10

y = (5/2)x - 5

m = 5/2

2 over -5.