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 $y=-3x-1$.