Question

1. x - 4y - 8 = 0

Explanation:

Step1: Isolate y - term

Start with the equation \( x - 4y - 8 = 0 \). First, we want to get the term with \( y \) by itself on one side. We can do this by subtracting \( x \) and adding 8 to both sides, or alternatively, move the \( x \) and \( - 8 \) to the other side. Let's rewrite the equation as \( - 4y=-x + 8 \) (by subtracting \( x \) from both sides and adding 8 to both sides, or simply moving \( x \) and \( - 8 \) to the right - hand side: \( - 4y=-x + 8 \)).

Step2: Solve for y

To solve for \( y \), we divide every term in the equation \( - 4y=-x + 8 \) by \( - 4 \).

When we divide \( - 4y\) by \( - 4 \), we get \( y \). When we divide \( -x\) by \( - 4 \), we get \( \frac{1}{4}x \). When we divide 8 by \( - 4 \), we get \( - 2 \). So the equation in slope - intercept form (\( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept) is \( y=\frac{1}{4}x-2 \).

If the problem was to rewrite the linear equation \( x - 4y-8 = 0 \) in slope - intercept form (or solve for \( y \)), this is the process.

Answer:

\( y=\frac{1}{4}x - 2 \)