Answer
Point-slope form:
$y+2=-4(x+3)$
Function notation of the slope-intercept form:
$f(x)=-4x-14$
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 (-3, -2). This means that the point-slope form of the line's equation is:
$y-(-2) = -4[x-(-3)]
\\y+2=-4(x+3)$
Convert the equation to slope-intercept form by isolating $y$ to obtain:
$y + 2 =-4(x+3)
\\y+2=-4\cdot x + (-4)\cdot 3
\\y+2=-4x+(-12)
\\y+2=-4x-12
\\y+2-2=-4x-12-2
\\y=-4x-14$
In function notation, the slope-intercept form of the equation is:
$f(x) = -4x-14$
