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To find the equation with the steepest graph, we need to examine the slope of each linear equation. In the form \( y = mx + b \), the slope of the line is given by \( m \). The larger the absolute value of \( m \), the steeper the line.

The equations provided are:

- \( A: y = -14x + 1 \) → Slope = -14
- \( B: y = \frac{3}{4}x - 9 \) → Slope = \( \frac{3}{4} \)
- \( C: y = 2x + 8 \) → Slope = 2
- \( D: y = 10x - 5 \) → Slope = 10

Among these, the largest absolute value of the slope is 14 (from \( A \: y = -14x + 1 \)), which means that equation A has the steepest graph.

The correct answer is **A**.

Would you like more details on slope and graph steepness? Here are five related questions to think about:

1. How does the slope of a line affect the angle it makes with the x-axis?
2. What is the graphical interpretation of a negative slope?
3. How would the graph change if the slope was a fraction like \( \frac{1}{2} \)?
4. How can you tell if two lines are parallel based on their slopes?
5. What is the difference between steepness and the y-intercept in a graph?

**Tip**: The greater the absolute value of the slope, the steeper the line. The sign of the slope only tells you the direction (positive slope rises, negative slope falls).

Learn how to determine which linear equation has the steepest graph by examining the slope in the form y = mx + b. This problem tests your understanding of slopes and their effect on the steepness of a graph. Suitable for students in Grades 8-10.

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