If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

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Class 11 | Maths | Miscellaneous Exercise | NCERT | Straight Lines

If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

GIVEN:

$y\text{ }=\text{ }3x\text{ }+\text{ }1\text{ }\ldots \text{ }\left( 1 \right)$

$2y\text{ }=\text{ }x\text{ }+\text{ }3\text{ }\ldots \text{ }\left( 2 \right)$

$y\text{ }=\text{ }mx\text{ }+\text{ }4\text{ }\ldots \text{ }\left( 3 \right)$

Here the slants of

Line (1),

$m1\text{ }=\text{ }3$

Line (2),

$m2\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}$

Line (3),

$m3\text{ }=\text{ }m$

We realize that the lines (1) and (2) are similarly disposed to line (3) which implies that the point between lines (1) and (3) rises to the point between lines (2) and (3).

NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines image - 74

On additional estimation

$\text{ }m2\text{ }+\text{ }m\text{ }+\text{ }6\text{ }=\text{ }1\text{ }+\text{ }m\text{ }\text{ }6m2$

So we get

$5m2\text{ }+\text{ }5\text{ }=\text{ }0$

Separating the condition by 5

$m2\text{ }+\text{ }1\text{ }=\text{ }0$

$m\text{ }=\text{ }\surd -1$

, which isn’t genuine.

Hence, this case is beyond the realm of imagination.

On the off chance that

NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines image - 75

i

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