Which equation has the steepest graph?A.y = x - 9B.y = 2x + 8C.y = 10x - 5D.y = -14x + 1SUBMITarrow_backPREVIOUS

To determine which equation has the steepest graph, we need to analyze the slopes of the lines represented by each equation.

1. ### Break Down the Problem

We are given four linear equations and need to identify which one has the greatest absolute slope.

2. ### Relevant Concepts

In the linear equation form $y = mx + b$, $m$ represents the slope of the line. The steeper the slope, the larger the absolute value of $m$.

3. ### Analysis and Detail

Let's extract the slopes from the equations provided:

• A. $y = x - 9$ → slope $m = 1$
• B. $y = 2x + 8$ → slope $m = 2$
• C. $y = 10x - 5$ → slope $m = 10$
• D. $y = -14x + 1$ → slope $m = -14$ (steepness is considered with absolute value)

Now, let's find the absolute values of each slope:

• |1| (from A) = 1
• |2| (from B) = 2
• |10| (from C) = 10
• |-14| (from D) = 14

4. ### Verify and Summarize

Among the absolute values calculated, the greatest is |−14| = 14, indicating that the line represented by the equation in option D is the steepest.

Final Answer

The equation with the steepest graph is D. $y = -14x + 1$.