The equation you provided is:

\[
2x - y = 5
\]

This is a linear equation in two variables, \(x\) and \(y\). To explore it further, you can:

1. **Solve for \(y\)** in terms of \(x\):  
   \[
   y = 2x - 5
   \]
   This is the slope-intercept form, \(y = mx + b\), where the slope \(m = 2\) and the y-intercept is \(-5\).

2. **Solve for \(x\)** in terms of \(y\)**:  
   \[
   x = \frac{y + 5}{2}
   \]

3. **Graph the equation**: The graph of this equation would be a straight line with a slope of 2 and a y-intercept at \(-5\).

4. **Find the intercepts**:
   - To find the x-intercept (where \(y = 0\)):
     \[
     2x - 0 = 5 \implies x = \frac{5}{2}
     \]
   - To find the y-intercept (where \(x = 0\)):
     \[
     2(0) - y = 5 \implies y = -5
     \]

Would you like more details or have any questions on this?

Here are 5 questions to further explore this equation:

1. How would you graph this equation on a coordinate plane?
2. What happens to the slope if the equation changes to \(2x - y = 10\)?
3. How would you find the solution to this equation if another equation is given?
4. Can you solve this equation using matrices or determinants?
5. What is the effect of multiplying both sides of the equation by a constant?

**Tip**: When solving for a variable, isolating it on one side of the equation helps to make the relationship between variables clear.

Explore the linear equation 2x - y = 5, including its slope, intercepts, and graph. Learn how to solve for y in terms of x, and vice versa, and find both x- and y-intercepts. Ideal for students in Grades 6-8 looking to master linear equations and graphing.

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