Hey there!
This linear equation is written in standard form, a form in which it's quite easy to find intercepts for one main reason. This reason revolves around zeros. When you see an x intercept, there's always a zero for the y, and when there's a y you see a zero for the x. Therefore, we can do this to get the intercepts.
For x:
2x-5(0) =10
2x = 10
x = (5,0)
For y:
2(0) -5y = 10
-5y=10
y= (0,-2)
Now, to find the slope, we can easily convert it to slope intercept form:
y = mx+b
Where m is the slope and b is he y intercept.
2x-5y=10
-5y=-2x+10
y = 2/5x-2
(notice how we divided both sides by -5)
Therefore, our slope is 2/5. Hope this helps!