To write the equation [tex]\(4y - 20x = 8\)[/tex] in slope-intercept form (which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept), follow these steps:
1. Isolate the [tex]\(y\)[/tex]-term on one side of the equation:
[tex]\[ 4y - 20x = 8 \][/tex]
Add [tex]\(20x\)[/tex] on both sides to isolate the [tex]\(y\)[/tex]-term:
[tex]\[ 4y = 20x + 8 \][/tex]
2. Solve for [tex]\(y\)[/tex] by dividing every term by 4:
[tex]\[ y = \frac{20x + 8}{4} \][/tex]
3. Simplify the expression:
[tex]\[ y = \frac{20x}{4} + \frac{8}{4} \][/tex]
[tex]\[ y = 5x + 2 \][/tex]
Thus, the equation in slope-intercept form is [tex]\(y = 5x + 2\)[/tex].
Therefore, the correct choice is:
[tex]\[
\boxed{y = 5x + 2}
\][/tex]
Choices (B) and (C) both represent the correct answer in this problem context. The most appropriate selection based on this detailed solution is:
[tex]\[
\boxed{B}
\][/tex]
