Hi!
Let's write it in slope intercept form first.
y = mx + b
Subtract y intercepts
1 - (-2) = 3
Subtract x intercepts
2 - (-3) = 5
y = 3/5x + b
Substitute one of the points to find y intercept.
1 = 3/5 · 2 + b
1 = 1.2 + b
-0.2 = b
y = 3/5x - 0.2
Now substitute the point (5,3), and if the equation is still correct, then it does pass through that point.
5 = 3/5 · 3 - 0.2
5 = 1.8 - 0.2
5 = 1.6
Since the equation is in correct, the line does NOT pass through the point (5,3).
Hope this helps! :)