Answer
y = -3x - 13/4
Step-by-step explanation
Equation of a line in slope-intercept form
[tex]y=mx+b[/tex]
where m is the slope and (0, b) is the y-intercept.
Substituting into the general equation with m = -3 and the point (1/4, -4), that is, x = 1/4 and y = -4, and solving for b:
[tex]\begin{gathered} -4=(-3)\cdot\frac{1}{4}+b \\ -4=-\frac{3}{4}+b \\ -4+\frac{3}{4}=-\frac{3}{4}+b+\frac{3}{4} \\ -\frac{13}{4}=b \end{gathered}[/tex]
Substituting into the general equation with m = -3 and b = -13/4, we get:
[tex]\begin{gathered} y=(-3)x+(-\frac{13}{4}) \\ y=-3x-\frac{13}{4} \end{gathered}[/tex]
