Question

Which has a greater rate of change?
Explain your answer

y = 3x - 4

Or

X -7 -5 -3 -1 1 3
y -10 -6 -2 2 6 10

Answer 1

To determine which has a greater rate of change, we can analyze the two equations and the data provided.

1. **For the equation \( y = 3x - 4 \)**:
- The rate of change is represented by the coefficient of \( x \) in the equation, which is 3. This means that for every increase of 1 in \( x \), \( y \) increases by 3.

2. **For the set of points provided:**
- The points given are:
\[
\begin{array}{c|c}
x & y \\
\hline
-7 & -10 \\
-5 & -6 \\
-3 & -2 \\
-1 & 2 \\
1 & 6 \\
3 & 10 \\
\end{array}
\]
- To find the rate of change, we can calculate the change in \( y \) over the change in \( x \) between two consecutive points or from any two points.

Let's choose the first and last points:
- From \( (-7, -10) \) to \( (3, 10) \):
- Change in \( x = 3 - (-7) = 10 \)
- Change in \( y = 10 - (-10) = 20 \)
- Rate of change = \(\frac{\Delta y}{\Delta x} = \frac{20}{10} = 2\)

For another example, consider two adjacent data points:
- From \( (-1, 2) \) to \( (1, 6) \):
- Change in \( x = 1 - (-1) = 2 \)
- Change in \( y = 6 - 2 = 4 \)
- Rate of change = \(\frac{4}{2} = 2\)

In various cases evaluated, the rate of change from the data points consistently equals 2.

### Conclusion
- The equation \( y = 3x - 4 \) has a rate of change of 3.
- The provided data points have a maximum rate of change of 2.

Therefore, the equation \( y = 3x - 4 \) has a greater rate of change than the data points provided.