Answer
$3x+y+2=0$
Work Step by Step
$x$-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:
$3x+y+2=0$
