## Calculus 10th Edition

$3x+y+2=0$
$x$-intercept: $(-\frac{2}{3},0)$ $;$ $y$-intercept: $(0,-2)$ The line with intercepts $(a,0)$ and $(0,b)$ has the equation $\dfrac{x}{a}+\dfrac{y}{b}=1$ In this case, $a=-\dfrac{2}{3}$ and $b=-2$. Substitute them into the equation: $\dfrac{x}{\Big(-\dfrac{2}{3}\Big)}+\dfrac{y}{-2}=1$ Simplify: $-\dfrac{3}{2}x-\dfrac{1}{2}y=1$ Multiply the whole equation by $-2$: $-2\Big(-\dfrac{3}{2}x-\dfrac{1}{2}y=1\Big)$ $3x+y=-2$ Take all terms to the left side to represent the equation in general form: $3x+y+2=0$