Q.A line makes intercepts $4$ and $-6$ on the x-axis and y-axis respectively. Find its equation. Verify your answer by finding the x- and y-intercepts of the line $3x - 2y - 12 = 0$ and comparing.

[!TLDR] Substitute $a=4,b=-6$ into $\dfrac{x}{a}+\dfrac{y}{b}=1$; the resulting equation matches $3x-2y-12=0$ exactly, so the intercepts of that equation must be $4$ and $-6$ — confirmed by direct substitution. …

Intercept form with $a=4,\,b=-6$: $\dfrac{x}{4}+\dfrac{y}{-6}=1$. Multiply through by $12$ (LCM of $4,6$): $3x - 2y = 12$, i.e. $3x-2y-12=0$. To verify, find the intercepts of $3x-2y-12=0$ directly: setting $y=0$ gives $3x=12 \implies x=4$ (the x-intercept), and setting $x=0$ gives $-2y=12 \implies y=-6$ (the y-intercept). These ex …

Substitute the given intercepts into $\dfrac{x}{a}+\dfrac{y}{b}=1$ and clear denominators; verify by finding the intercepts of the resulting equ …

A sign slip on the negative intercept $b=-6$ — writing $\dfrac{x}{4}+\dfrac{y}{6}=1$ instead of $\dfrac{x}{4}+\dfrac{y}{-6}=1$ — gives the wrong li …