We need to determine the equation of the line that passes through (0, -4) and has a slope of -1/4. For that we will first use the slope-point form, and then isolate the y-variable on the left side to determine the slope-intercept form. The two forms are shown below:
[tex]\begin{gathered} y-y_1=m\cdot(x-x_1) \\ y=m\cdot x+b \end{gathered}[/tex]Since we have the value of the slope, and a point we can determine the first equation.
[tex]\begin{gathered} y-(-4)=-\frac{1}{4}\cdot(x-0) \\ y+4=-\frac{1}{4}x \\ \end{gathered}[/tex]Now we need to isolate the y-variable on the left side.
[tex]y=-\frac{1}{4}x-4[/tex]
