Answer
Point-slope form:
$y-1=8(x+4)$
Function form of the slope-intercept form:
$f(x)=8x+33$
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=8 and passes through the point (-4, 1). This means that the point-slope form of the line's equation is:
$y-1 = 8[x-(-4)]
\\y-1=8(x+4)$
Convert the equation to slope-intercept form by isolating $y$ to obtain:
$y - 1 =8(x+4)
\\y-1=8\cdot x + 8\cdot 4
\\y-1 =8x+32
\\y-1+1=8x+32+1
\\y=8x+33$
In function notation, the slope-intercept form of the equation is:
$f(x) = 8x+33$
