Let's analyze the given savings function rule for Ali:
[tex]\[ y = 5x + 25 \][/tex]
Here, \( y \) represents Ali's total savings after \( x \) weeks.
1. Identifying the Rate of Change:
- The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope of the line (the rate of change), and \( b \) is the y-intercept (the initial value).
- In Ali's savings function \( y = 5x + 25 \):
- The coefficient of \( x \) is 5. This coefficient represents the rate of change.
Therefore, the rate of change of this function is:
[tex]\[ 5 \][/tex]
Hence, the first blank is filled with:
[tex]\[ 5 \checkmark \][/tex]
2. Nature of the Rate of Change:
- The rate of change here is constant because the slope \( m = 5 \) does not change; it remains the same regardless of the value of \( x \).
Therefore, the second blank is filled with:
[tex]\[ constant \][/tex]
3. Type of Graph:
- Since the rate of change (slope) is constant, the relationship between \( x \) (weeks) and \( y \) (savings) is linear. This means that the graph of this function is a straight line.
Therefore, the third blank is filled with:
[tex]\[ straight line \][/tex]
Putting it all together, the completed answer is:
The rate of change of this function is \( 5 \checkmark \).
Because this function has a [tex]\( constant \)[/tex] rate of change, the graph of this function is a [tex]\( straight line \)[/tex].
