Ali currently has [tex]$25. He is going to start saving $[/tex]5 every week. Ali's savings function rule is [tex]y = 5x + 25[/tex].

The rate of change of this function is \(\square\) \(\checkmark\).

Complete:
Because this function has a [tex]\(\square\)[/tex] rate of change, the graph of this function is a [tex]\(\square\)[/tex].



Answer :

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].