Question

1. solve the equation for y and identify the slope: 2x - 4y = 8

Explanation:

Step1: Isolate the term with y

We start with the equation \(2x - 4y = 8\). Subtract \(2x\) from both sides to get \(-4y=-2x + 8\).

Step2: Solve for y

Divide every term by \(-4\). So \(y=\frac{-2x}{-4}+\frac{8}{-4}\), which simplifies to \(y = \frac{1}{2}x-2\).

Step3: Identify the slope

In the slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), for the equation \(y=\frac{1}{2}x - 2\), the slope \(m=\frac{1}{2}\).

Answer:

The solution for \(y\) is \(y=\frac{1}{2}x - 2\) and the slope is \(\frac{1}{2}\).