y<− 
3
1
​
 x+6
y, is less than, 6, x, minus, 1
y<6x−1


The given inequality is:

\[
y < 6x - 1
\]

This represents a linear inequality, where \(y\) is less than the expression \(6x - 1\). Here's what it means:

### Graphical Interpretation:
1. The boundary line of this inequality is the line \(y = 6x - 1\).
2. Since the inequality is a strict "<" (less than), the region below the line \(y = 6x - 1\) represents the solution to the inequality.
3. The line itself is not included in the solution (hence it is drawn as a dashed line on the graph).

### Key Features of the Line \(y = 6x - 1\):
- **Slope**: The slope is \(6\), which means for every unit increase in \(x\), \(y\) increases by 6 units.
- **Y-intercept**: The line crosses the \(y\)-axis at \(-1\).

### Solving the inequality for a specific value:
If you want to check if a specific point \((x, y)\) satisfies the inequality, you can plug the values of \(x\) and \(y\) into the inequality and verify if the statement holds.

Would you like more details on how to graph this inequality or solve similar problems?

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### Follow-up questions:
1. How would you graph the solution to this inequality?
2. What is the meaning of the slope and intercept in this context?
3. How would the inequality change if it were \(y \leq 6x - 1\)?
4. How can you test if a point lies in the solution set?
5. How would the graph change if the inequality was \(y > 6x - 1\)?

### Tip:
To graph linear inequalities, always start by graphing the boundary line and then shading the appropriate side based on the inequality sign.

Learn how to graph and solve the linear inequality y < 6x - 1. This problem includes key algebraic concepts like the slope-intercept form and linear inequality graphing techniques. Suitable for students in Grades 8-10.

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