Answer
Point-slope form"
$y+4=-(x+\frac{1}{4})$
Function notation of the slope-intercept form:
$f(x)=-x-\frac{17}{4}$
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 $(-\frac{1}{4}, -4)$. This means that the point-slope form of the line's equation is:
$y-(-4) = -1[x-(-\frac{1}{4})]
\\y+4=-(x+\frac{1}{4})$
Convert the equation to slope-intercept form by isolating $y$ to obtain:
$y + 4 =-(x+\frac{1}{4})
\\y+4=-1\cdot x + (-1)\cdot \frac{1}{4}
\\y+4=-x+(-\frac{1}{4})
\\y+4=-x-\frac{1}{4}
\\y+4-4=-x-\frac{1}{4}-4
\\y=-x-\frac{1}{4} - \frac{16}{4}
\\y=-x-\frac{17}{4}$
In function notation, the slope-intercept form of the equation is:
$f(x) = -x-\frac{17}{4}$
