Q.Reduce the equation $2x + 3y - 6 = 0$ to intercept form, and find the intercepts made by the line on the axes.

[!TLDR] Divide $2x+3y-6=0$ by the constant $6$ to reach $\dfrac{x}{3}+\dfrac{y}{2}=1$ directly. [!ANSWER] $\dfrac{x}{3}+ …

$2x+3y-6=0 \implies 2x+3y=6$. Dividing throughout by $6$: $\dfrac{2x}{6}+\dfrac{3y}{6}=1 \implies \dfrac{x}{3}+\dfrac{y}{2}=1$. Comparing with $\dfrac{x}{a}+\dfrac{y}{b}=1$: x-intercept $a=3$, y-intercept $b=2$. Check directly: setting $y=0$ in the original equation gives $2x=6 \im …

Move the constant to the right-hand side, then divide throughout by that constant so th …

Dividing $2x$ by $6$ but forgetting to also divide $3y$ by $6$ (only simplifying one term) is a com …