(a) \( x-2 y=4 \)

Did you know that the equation \( x - 2y = 4 \) represents a straight line in the Cartesian plane? To put it in slope-intercept form, you can rearrange it to \( y = \frac{1}{2}x - 2 \), where the slope is \( \frac{1}{2} \) and the y-intercept is \(-2\). This means for every unit you move to the right along the x-axis, you move up half a unit! Now, if you're solving for \( x \) and \( y \), a common mistake to watch out for is forgetting to consider both variables. When isolating either variable, make sure to double-check your arithmetic; one tiny slip could lead to a completely different line! For example, when substituting y-value solutions back into the original equation, always verify the equality holds true.