Mathematics

$$2x+3y=7$$ and $$2x+3y=12$$ are two parallel staright lines, then where does the point $$(1,3)$$ lies.


SOLUTION
Given: $$2x+3y = 7$$      $$2x+3y=12$$
Let $$L_1 \to 2x+3y-7=0$$           $$L_2\to 2x+3y-12=0$$
Let given point $$P(1,3)$$
If $$L_1(P) \times L_2(P) < 0$$  Point lies between lines
otherwise not between lies
$$L_1 (P) = 2(1) + 3(3) - 7 = 4$$
$$L_2(P) = 2(1) + 3(3)-12 = -1$$
$$L_1(P) \times L_2(P) = 4 \times -1 = -4 < 0$$
So point lies between the lines.
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