Answer
Point-slope form:
$y+4=-6(x+2)$
Function notation of the slope-intercept form:
$f(x) = -6x-16$
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 $m=-6$ and passes through the point (-2, -4). This means that the point-slope form of the line's equation is:
$y-(-4) = -6[x-(-2)]
\\y+4=-6(x+2)$
Convert the equation to slope-intercept form by isolating $y$ to obtain:
$y +4 =-6(x+2)
\\y+4=-6\cdot x + (-6)\cdot 2
\\y+4=-6x+(-12)
\\y+4=-6x-12
\\y+4-4=-6x-12-4
\\y=-6x-16$
In function notation, the slope-intercept form of the equation is:
$f(x) = -6x-16$
