Find the equation of the line passing through the point $(1, 4)$ and intersecting the line $x - 2 y - 11 = 0$ on the x-axis.

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Solution

As the line meets $x - 2 y - 11 = 0$ at x-axis Then y=0 should be given in
$x - 2 * 0 - 11 = 0 \Rightarrow x = 11$
Hence, they will meet at $(11, 0)$
Now, Slope of required line $m = \frac{4 - 0}{1 - 11} = - \frac{2}{5}$
Hence, We can write equation as $y - 0 = - \frac{2}{5} (x - 11) \Rightarrow 5 y = - 2 x + 11 \Rightarrow 2 x + 5 y - 11 = 0$

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Find the equation of the line passing through the point (1,4) and intersecting the line x−2y−11=0 on the x-axis.

As the line meets x−2y−11=0 at x-axis Then y=0 should be given inx−2∗0−11=0⇒x=11Hence, they will meet at (11,0)Now, Slope of required line m=4−01−11=−25Hence, We can write equation as y−0=−25(x−11)⇒5y=−2x+11⇒2x+5y−11=0

Find the equation of the line passing through the point $(1, 4)$ and intersecting the line $x - 2 y - 11 = 0$ on the x-axis.