Answer
$y=-3x-1$
Work Step by Step
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 satisfy the equation of the line.
Substitute the $x$ and $y$ coordinates of the given point into the tentative equation above to find $b$:
$y=-3x+b
\\-4 = -3(1) + b
\\-4 =-3 + b
\\-4+3 = b
\\-1=b.$
Thus, the equation of the line is $y=-3x-1$.
