Answer
$a)$ $y=-\dfrac{1}{2}x$
$b)$ $x+2y=0$
$c)$ Graph below
Work Step by Step
The line that has slope $-\dfrac{1}{2}$ and passes through the point $(6,-3)$
$a)$
The point-slope form of the equation of a line is $y-y_{1}=m(x=x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is its slope.
Both the slope of the line and a point through which it passes are given.
Substitute them into the point-slope form of the equation of a line formula and simplify:
$y-(-3)=-\dfrac{1}{2}(x-6)$
$y+3=-\dfrac{1}{2}x+3$
To represent the equation in slope-intercept form, solve for $y$:
$y=-\dfrac{1}{2}x+3-3$
$y=-\dfrac{1}{2}x$
$b)$
To represent the equation in general form, begin by moving $-\dfrac{1}{2}$ to the left side:
$\dfrac{1}{2}x+y=0$
Multiply the whole equation by $2$:
$2\Big(\dfrac{1}{2}x+y=0\Big)$
$x+2y=0$
$c)$ Graph below
