Straight LineHardBloom L3
Question
The number of integral values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer is :
Options
A.2
B.0
C.4
D.1
Solution
Sol. [Key Concept: Integer $x$ at the intersection of $3x + 4y = 9$ and $y = mx + 1$ ⇒ count $m$ by divisibility.]
For point of intersection,
$$\begin{matrix} & 3x + 4mx + 4 = 9 \\ \Rightarrow \ & x = \frac{5}{3 + 4m} \\ & 3 + 4m = \pm 1, \pm 5 \\ \Rightarrow \ & m = - 1/2, - 1,1/2, - 2 \end{matrix}$$
Number of integral values of $m = 2$
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