Answer
$x+2y+6=0$
Work Step by Step
$x$-intercept: $-6$ $,$ $y$-intercept: $-3$
The line's intercepts are given. These represent the points $(-6,0)$ and $(0,-3)$.
Find the slope of the line substituting its intercepts into the formula $m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$:
$m=\dfrac{-3-0}{0-(-6)}=\dfrac{-3}{6}=-\dfrac{1}{2}$
The point-slope form of the equation of a line is $y=mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept.
Both the slope of the line and its $y$-intercept are known. Substitute them into the formula and simplify:
$y=-\dfrac{1}{2}x-3$
Multiply the whole equation by $2$:
$2\Big(y=-\dfrac{1}{2}x-3\Big)$
$2y=-x-6$
Take all terms to the left side:
$x+2y+6=0$
