One way to show a function is 1-1 is to show that if two outputs are the same, then the inputs had to have been the same as well:
If f(a) = f(b), then a=b.
If you can show this, you've shown that each output is paired with a unique input, so the function is 1-1.
For this function, we'd first start assuming that f(a) = f(b):
f(a) = f(b)
-3a+5 = -3b+5
Now we'll solve this for a:
-3a + 5 = -3b + 5
-3a + 5 - 5 = -3b + 5 - 5
-3a = -3b
-3a ÷ (-3) = -3b ÷ (-3)
a = b
This shows that the only way the outputs are the same is if the inputs are the same, which means each output comes from a unique input, so the function is 1-1.