If $m$ and $b$ are real numbers and $mb 0$, then the line whose equation is $y = mx + b$ cannot

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If $m$ and $b$ are real numbers and $mb > 0$, then the line whose equation is $y = mx + b$ cannot contain the point:

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Sol. [Key Concept: A line $y = mx + b$ through $(x_{0,0)}$ gives $mb = - m^{2}x_{0}$; with $mb > 0$ a point with positive $x$-intercept cannot lie on it.]$$mb > 0 \Rightarrow m > 0 $$and $b > 0$ or $m < 0$ and $b < 0$Hence possible lines are as shownIn both the cases $x$ intercept cannot be +ve⇒ (b)

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