Answer
point-slope form: $y+2=-(x+\frac{1}{2})$
slope-intercept form: $y=-x-2.5$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where m = slope and b = y-intercept
(2) The point-slope form of a line's equation is:
$y-y_1=m(x-x_1)$
(a) point-slope form
The given line has a slope of $-1$ and passes through the point $(-\frac{1}{2}, -2)$.
Substitute these values into the point-slope form above to obtain:
$y-(-2)=-1[x-(-\frac{1}{2})]
\\y+2 = -(x+\frac{1}{2})$
(b) slope-intercept form
Substitute the slope $-1$ to $m$ to obtain the tentative equation:
$y=-x+b$
The line passes through $(-\frac{1}{2}, -2)$.
This means that the coordinates of this point satisfy the equation of the line. Substitute the x and y-coordinates of this point into the tentative equation to obtain:
$y=-x+b
\\-2 = -(-\frac{1}{2}) + b
\\-2 = \frac{1}{2} + b
\\-2-\frac{1}{2}= b
\\-2.5 = b$
Thus, the equation of the line is $y=-x-2.5$.
