The equation $x + 2y = 4$ is a linear equation in two variables, $x$ and $y$. It can represent a straight line in a two-dimensional coordinate plane. Here's a breakdown of how to approach it:

1. Solve for $y$ in terms of $x$:

To express $y$ in terms of $x$, rearrange the equation: $2y = 4 - x$ $y = \frac{4 - x}{2}$ $y = -\frac{1}{2}x + 2$

2. Solve for $x$ in terms of $y$:

Rearrange the equation to express $x$ in terms of $y$: $x = 4 - 2y$

3. Graphical Representation:

This equation represents a line with:

• Slope ($m$): $-\frac{1}{2}$
• y-Intercept: $2$ (point where $x = 0$)
• x-Intercept: $4$ (point where $y = 0$)

4. Example Points:

You can find points on the line by substituting values of $x$ or $y$:

• When $x = 0$, $y = 2$.
• When $x = 4$, $y = 0$.
• When $x = 2$, $y = 1$.

Would you like a graph, or do you have more specific questions about this equation?

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Related Questions:

1. How do you determine if a point lies on this line?
2. What are the applications of such linear equations in real-life contexts?
3. How does changing the coefficients in the equation affect the slope and intercept?
4. How do you find the distance of a point from this line?
5. What is the relationship between this line and another line parallel to it?

Tip:

For linear equations, understanding the slope and intercept simplifies graphing and interpretation.