Question

Find the intercepts made by the line on
the axes which pass through the point (5,-2) andhas slope 5/2​

Answer 1

$Let \: a \: point \: (x_{1},y_{1}) = (5,-2), \:and \\ Slope (m) = \frac{5}{2}$

$\underline { \pink { Point - Slope \:of \: \:the \:Equation }}$

$\boxed { \orange { y - y_{1} = m(x-x_{1}) }}$

$\implies y - (-2) = \frac{5}{2} ( x - 5 )$

$\implies 2(y - 2 ) = 5(x - 5)$

$\implies 2y - 4 = 5x - 25$

$\implies 0 = 5x - 25 - 2y + 4$

$\implies 5x - 2y = 21$

/* Divide each term by 21 , we get */

$\implies \frac{5x}{21} + \frac{-2y}{21} = \frac{21}{21}$

$\implies \frac{x}{\frac{21}{5}} + \frac{y}{\frac{-21}{2}} = 1$

$Compare \: this \: with \\ \blue { Two \:intercepts \: form }$

$\pink { \frac{x}{a} + \frac{y}{b} = 1 }$

$Where , \blue { x - intercept = a },\\\blue { y - intercept = b}$

Therefore.,

$\blue { x - intercept ( a )}\green { = \frac{21}{5}}$

$\blue { y - intercept = b}\green { = \frac{-21}{2}}$

•••♪