Question

If the line 4x – 6y – 24 = 0 is written in the form xa+yb=1, then value of 3a – 2b =​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Line is 4x-6y-24=0}$

$\underline{\textbf{To find:}}$

$\textsf{The value of 3a-2b when the equation is written}$

$\textsf{in intercept form}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\textsf{4x-6y-24=0}$

$\textsf{This can be written as}$

$\textsf{4x-6y=24}$

$\textsf{Divide by 24 on bothsides, we get}$

$\mathsf{\dfrac{4x}{24}-\dfrac{6y}{24}=\dfrac{24}{24}}$

$\mathsf{\dfrac{x}{6}-\dfrac{y}{4}=1}$

$\mathsf{\dfrac{x}{6}+\dfrac{y}{-4}=1}$

$\mathsf{Comparing\;with\;\dfrac{x}{a}+\dfrac{y}{b}=1\;we\;get}$

$\mathsf{a=6\;and\;b=-4}$

$\mathsf{Now,}$

$\mathsf{3a-2b}$

$\mathsf{=3(6)-2(-4)}$

$\mathsf{=18+8}$

$\mathsf{=26}$

$\implies\boxed{\mathsf{3a-2b=26}}$

$\underline{\textbf{Find more:}}$

Area of ​​a triangle formed by x-axis, y-axis and line x + y = 8 is  

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