The slopes of the equations must be different:
y1= a*x + b
y2 = c*x + b
then a ≠ c
A linear function is:
Y = a*x + b
now, suppose we have other linear function
H = c*x + d
Let's find the condition needed to have an intersection of these two lines, or:
a*x + b = c*x + d
(a - c)*x = d - b
Where a, c, d and b are real numbers.
You can see that the only condition is that the coefficient that multiplicates the variable (x) must be different than 0 (because if it is 0, the x vanishes and we can never solve the equation)
So we must have that the slopes of the two linear equations need to be different.