Answer
Point-slope form:
$y+\frac{1}{2} = -(x+2)$
Function notation of the slope-intercept form:
$f(x) = -x -\frac{5}{2}$
Work Step by Step
RECALL:
(i) The point-slope form of a line's equation is:
$y-y_1=m(x-x_1)$
where
m= slope and $(x_1, y_1)$ is a point on the line.
(ii) The function notation of the slope-intercept form of a line's equation is:
$f(x) = mx + b$
where
m= slope and b = y-intercept
The given line has $m=-1$ and passes through the point $(-2, -\frac{1}{2})$. This means that the point-slope form of the line's equation is:
$y-(-\frac{1}{2}) = -1[x-(-2)]
\\y+\frac{1}{2}=-(x+2)$
Convert the equation to slope-intercept form by isolating $y$ to obtain:
$y + \frac{1}{2} =-(x+2)
\\y+\frac{1}{2}=-1\cdot x + (-1)\cdot 2
\\y+\frac{1}{2}=-x+(-2)
\\y+\frac{1}{2}=-x-2
\\y+\frac{1}{2}-\frac{1}{2}=-x-2-\frac{1}{2}
\\y=-x -\frac{4}{2} - \frac{1}{2}
\\y=-x-\frac{5}{2}$
In function notation, the slope-intercept form of the equation is:
$f(x) = -x-\frac{5}{2}$
