Answer :
To determine the rate of change of Ali's Savings Function, we can analyze the function given: \( y = 5x + 25 \).
1. Identify the Components:
The function \( y = 5x + 25 \) is a linear function in the form of \( y = mx + b \), where \( m \) represents the slope (or rate of change), and \( b \) represents the y-intercept.
2. Understand the Context:
- \( y \) represents Ali's total savings.
- \( x \) represents the number of weeks.
- \( 25 \) is the initial amount of money Ali already has.
- \( 5 \) represents the amount Ali saves every week.
3. Determine the Rate of Change:
The rate of change in this linear function is given by the slope \( m \).
4. Identify the Slope:
By comparing the given function to the slope-intercept form \( y = mx + b \):
- The coefficient of \( x \) is \( 5 \).
So, the rate of change for Ali's savings function is [tex]\( \boxed{5} \)[/tex]. This means for every week that passes, Ali's savings will increase by [tex]\( \$5 \)[/tex].
1. Identify the Components:
The function \( y = 5x + 25 \) is a linear function in the form of \( y = mx + b \), where \( m \) represents the slope (or rate of change), and \( b \) represents the y-intercept.
2. Understand the Context:
- \( y \) represents Ali's total savings.
- \( x \) represents the number of weeks.
- \( 25 \) is the initial amount of money Ali already has.
- \( 5 \) represents the amount Ali saves every week.
3. Determine the Rate of Change:
The rate of change in this linear function is given by the slope \( m \).
4. Identify the Slope:
By comparing the given function to the slope-intercept form \( y = mx + b \):
- The coefficient of \( x \) is \( 5 \).
So, the rate of change for Ali's savings function is [tex]\( \boxed{5} \)[/tex]. This means for every week that passes, Ali's savings will increase by [tex]\( \$5 \)[/tex].
