Question

Which has a greater rate of change?
Explain your answer

y = 2/3x +5

Answer 1

To determine the rate of change of the equation \( y = \frac{2}{3}x + 5 \), we start by identifying the slope of the line. In the slope-intercept form of a linear equation, \( y = mx + b \), the slope \( m \) represents the rate of change.

In this equation:
- \( m = \frac{2}{3} \)
- \( b = 5 \) (the y-intercept, which does not affect the rate of change)

The slope \( \frac{2}{3} \) indicates that for every increase of 1 unit in \( x \), \( y \) increases by \( \frac{2}{3} \) units.

If you want to compare this rate of change with a different linear equation, you would need the slope of that equation.

For instance, if you had another linear equation such as \( y = 4x + 1 \), the slope (rate of change) is \( 4 \), which is greater than \( \frac{2}{3} \).

### Conclusion:
- The rate of change of the given equation \( y = \frac{2}{3}x + 5 \) is \( \frac{2}{3} \).
- To determine if this is greater or lesser than another rate of change, compare it with the slope of the other equation.

If comparing to just one equation, provide that equation to make a complete comparison.