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To determine the correct graph for the equation \( y = 82x + 175 \), let’s analyze its properties:

1. **Slope (m)**: The coefficient of \( x \) is \( 82 \), indicating a steep, positive slope.
2. **Y-intercept (b)**: The constant term \( 175 \) is the y-intercept, meaning the graph should cross the y-axis at \( y = 175 \).

### Analyzing the Options:
Since the slope is positive, the line should rise from left to right. This immediately eliminates options **A** and **C**, as they show lines with negative slopes (falling from left to right). Between **B** and **D**, both have positive slopes, but **B** has a steeper slope that matches the steepness indicated by \( 82 \). Additionally, both options have the y-intercept above zero, as expected.

### Conclusion:
The correct answer is **B**.

Would you like a further breakdown of how I reached this conclusion or have any additional questions?

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Here are 5 related questions for further practice:
1. How would the graph change if the slope was negative?
2. What effect does increasing the y-intercept have on the graph?
3. How would you find the x-intercept of the equation \( y = 82x + 175 \)?
4. How would this equation look in standard form \( Ax + By = C \)?
5. What would the graph look like if the equation were \( y = -82x + 175 \)?

**Tip:** For a steep line, focus on a larger change in the y-values for every unit increase in x.

Graph the following equation: y = 82x + 175. Use appropriate scales on each axis. Choose the correct graph from the given options.

Learn how to graph the linear equation y = 82x + 175 using slope-intercept form. This problem involves analyzing a steep positive slope (82) and identifying the y-intercept at 175. Suitable for students in Grades 8-10.

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