Answer
point-slope form: $y+\frac{1}{4}=-(x+4)$
slope-intercept form: $y=-x-4.25$
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 $(-4, -\frac{1}{4})$.
Substitute these values into the point-slope form above to obtain:
$y-(-\frac{1}{4})=-1[x-(-4)]
\\y+\frac{1}{4} = -(x+4)$
(b) slope-intercept form
Substitute the slope $-1$ to $m$ to obtain the tentative equation:
$y=-x+b$
The line passes through $(-4, -\frac{1}{4})$.
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:
$y=-x+b
\\-\frac{1}{4} = -(-4) + b
\\-\frac{1}{4} = 4 + b
\\-\frac{1}{4}-4= b
\\-4.25 = b$
Thus, the equation of the line is $y=-x-4.25$.
