Q.Reduce the equation $2x + 3y - 6 = 0$ to

Rearrange for $y$ to get the slope-intercept form, and divide through so the right side is $1$ to get the intercept form.

1. Slope-intercept form. Solve $2x + 3y - 6 = 0$ for $y$:

   $3y = -2x + 6 \ \Rightarrow\ y = -\dfrac{2}{3}x + 2$

   Comparing with $y = mx + c$: slope $m = -\dfrac{2}{3}$ and y-intercept $c = 2$.
2. Intercept form. Take the constant to the right and divide so the right side becomes $1$. From $2x + 3y = 6$, divide by $6$:

   $\dfrac{2x}{6} + \dfrac{3y}{6} = 1 \ \Rightarrow\ \dfrac{x}{3} + \dfrac{y}{2} = 1$

   Comparing with $\dfrac{x}{a} + \dfrac{y}{b} = 1$: x-intercept $a = 3$ and y-intercept $b = 2$. …

Forgetting to divide every term (including the constant) by $6$ when forming the intercept form, or misreading the y-intercept sign — f …