Answer
Point-slope form:
$y+3=-4x$
Function notation of the slope-intercept form:
$f(x)=-4x-3$
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 $m=-4$ and passes through the point (0, -3). This means that the point-slope form of the line's equation is:
$y-(-3) = -4[x-0]
\\y+3=-4(x)
\\y+3=-4x$
Convert the equation to slope-intercept form by isolating $y$ to obtain:
$y + 3=-4x
\\y+3-3=-4x-3
\\y=-4x-3$
In function notation, the slope-intercept form of the equation is:
$f(x) = -4x-3$
