The equation $2x - y = 4$ is a linear equation. Let's analyze it:

Solving for $y$ in terms of $x$:

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

This represents a line in slope-intercept form ($y = mx + b$), where:

• Slope ($m$): $2$
• Y-intercept ($b$): $-4$

Solving for $x$ in terms of $y$:

Rewriting to express $x$ in terms of $y$: $x = \frac{y + 4}{2}$

Key Points:

• The equation represents a straight line.
• The slope is $2$, indicating the line rises 2 units for every 1 unit it moves to the right.
• The y-intercept is $-4$, meaning the line crosses the $y$-axis at $(0, -4)$.

Graphing:

You can graph this line by:

1. Plotting the y-intercept ($0, -4$).
2. Using the slope ($2$) to find another point, e.g., moving up 2 units and 1 unit to the right from the intercept.

Would you like a graph or further explanation?

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Questions to Explore Further:

1. How can we find the x-intercept of $2x - y = 4$?
2. What are some real-world applications of linear equations like $2x - y = 4$?
3. How would you write this equation in standard form ($Ax + By = C$)?
4. What happens to the graph of the line if we increase the slope from $2$ to $3$?
5. Can you find the solution to $2x - y = 4$ for a specific value of $x$ (e.g., $x = 3$)?

Tip:

Remember that the slope-intercept form $y = mx + b$ is especially useful for graphing and visualizing the behavior of a line.