#### Answer

$y=-3x-1$

#### Work Step by Step

RECALL:
The slope-intercept form of a line's equation is $y=mx + b$, where m=slope and b=y-intercept.
The line has a slope of -3, so $m=-3$.
This means that the tentative equation of the line is $y=-3x+b$.
The line passes through the point (1,-4), which means that the coordinates of this point satisfies the equation of the line.
Substitute the x and y coordinates of the given point into the tentative equation above to have
$y=-3x+b
\\-4 = -3(1) + b
\\-4 =-3 + b
\\-4+3 = b
\\-1=b.$
Thus, the equation of the line is $y=-3x-1$.