Answer
Point-slope form:
$y-6=5(x+2)$
Function notation of the slope-intercept form:
$f(x) = 5x+16$
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=5 and passes through the point (-2, 6). This means that the point-slope form of the line's equation is:
$y-6 = 5[x-(-2)]
\\y-6=5(x+2)$
Convert the equation to slope-intercept form by isolating $y$ to obtain:
$y - 6 =5(x+2)
\\y-6=5\cdot x + 5\cdot 2
\\y-6 =5x+10
\\y-6+6=5x+10+6
\\y=5x+16$
In function notation, the slope-intercept form of the equation is:
$f(x) = 5x+16$
