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).