In this case, we'll have to carry out several steps to find the solution. 
Step 01:
Data
x=5|y|-3
Step 02:
Four points
If x = 0 : 
x = 5|y| - 3
0 = 5|y| - 3
3 = 5|y| - 3 + 3
3 / 5 = 5|y| / 5 
3/5 = |y|
| y | = 3/5 
y = 3/5 
y = -3/5 
If x = 1 :
x = 5|y| - 3 
1 = 5|y| - 3
1 + 3 = 5|y| - 3 + 3 
4 / 5 = 5 |y| / 5 
4/5 = |y| 
| y | = 4/5 
y = 4/5 
y = -4/5 
If x = 2 : 
x = 5|y| - 3 
2 = 5|y| - 3
2 + 3 = 5|y| - 3 + 3 
5 / 5 = 5 |y| / 5
1 = |y|
| y | = 1
y = 1
y = -1
If x = 3 
 
x = 5|y| - 3 
3 = 5|y| - 3
3 + 3 = 5|y| - 3 + 3 
6 / 5 = 5 |y| / 5
6/5 = |y|
| y | = 6/5
y = 6/5
y = -6/5
That is the full solution. 
Note: I solved the exercise with the published equation.