Answer:
The equation of the line in slope-intercept form is:
[tex]y=\frac{1}{2}x-4[/tex]and in standard form is:
[tex]x-2y=4[/tex]Explanation:
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]where m is the slope, and b is the y-intercept.
Since the line passes through (0, -4), we can use this point to obtain the value of the y-intercept by sustituting x = 0, y = -4 and m = 1/2 into the equation of the line.
[tex]\begin{gathered} -4=\frac{1}{2}(0)+b \\ \\ -4=b \end{gathered}[/tex]Therefore, the equation of the line in slope-intercept form is
[tex]y=\frac{1}{2}x-4[/tex]To write this in standard form, multiply both sides of the equation by 2
[tex]\begin{gathered} 2y=x-4 \\ \text{Subtract x from both sides} \\ 2y-x=-4 \\ Multiply\text{ both sides by -1} \\ x-2y=4 \end{gathered}[/tex]