#### Answer

The linear function is $f(x) = -3x+1$.
Refer to the graph below.

#### Work Step by Step

RECALL:
(1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $(x_1, y_1)$ is a point on the line and $m$ = slope of the line.
(2) The slope-intercept form of a line is $y=mx+b$ where $m$ = slope of the line and $b$ = y-intercept of the line.
The line has:
$m=-3$;
contains the point $(-1, 4)$
Use the point-slope form in (1) above to obtain the line's equation:
$y-4=-3[x-(-1)]
\\y-4=-3(x+1)$
Isolate $y$ on one side to get the slope-intercept form of the line's equation:
$y-4+4 = -3(x+1)+4
\\y=-3(x+1)+4
\\y=-3x-3+4
\\y=-3x+1$
Thus, the linear function is $f(x)=3x+1$
To graph the line, perform the following steps:
(1) Plot the y-intercept point $(0 ,1)$.
(2) Use the slope $-3$ or $\frac{-3}{1}$ to obtain another point on the line.
From $(0, 1)$, move 3 units down (the rise) and 1 unit to the right (the run) t arrive at the point $(1, -2)$.
(3) Connect the two points using a straight line to complete the graph.
(refer to the image in the answer part above for the graph)