Answer
Point-slope form:
$y-1=4(x-3)$
Slope-intercept form in function notation:
$f(x) = 4x-11$
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) Slope-intercept form in function notation has the equation:
$f(x) = mx + b$
where
m= slope and b = y-intercept
The given line has m=4 and passes through the point (3, 1). This means that the line's equation in point slope form is:
$y-1 = 4(x-3)$
Convert the equation to slope-intercept form by isolating $y$ to obtain:
$y -1=4(x-3)
\\y-1=4\cdot x - 4\cdot 3
\\y-1 =4x-12
\\y-1+1=4x-12+1
\\y=4x-11$
In function notation, the slope-intercept form of the equation is:
$f(x) = 4x -11$
