Find the intercepts cut off by the line $3 x - 4 y + 6 = 0$ on the axes.

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Solution

$x -$ intercept:Put $y = 0$

$∴ 3 x + 6 = 0$

$\Rightarrow x = \frac{- 6}{3} = - 2$ is the $x -$ intercept

$y -$ intercept:Put $x = 0$

$∴ - 4 y + 6 = 0$

$\Rightarrow y = \frac{- 6}{- 4} = \frac{3}{2}$ is the $y -$ intercept.

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For what values of a a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x - 3y + 6 = 0 on the axes.

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Find the intercepts cut off by the line 3x−4y+6=0 on the axes.

x−intercept:Put y=0∴3x+6=0⇒x=−63=−2 is the x−intercepty−intercept:Put x=0∴−4y+6=0⇒y=−6−4=32 is the y−intercept.

Find the intercepts cut off by the line $3 x - 4 y + 6 = 0$ on the axes.

$x -$ intercept:Put $y = 0$

$∴ 3 x + 6 = 0$

$\Rightarrow x = \frac{- 6}{3} = - 2$ is the $x -$ intercept

$y -$ intercept:Put $x = 0$

$∴ - 4 y + 6 = 0$

$\Rightarrow y = \frac{- 6}{- 4} = \frac{3}{2}$ is the $y -$ intercept.