Question

use the graph below for questions 1 - 7.

1. what is this situation about?

britney is saving her money. the graph shows how much money she has in her coin bank each week.

1. what are the intervals of the x - axis and y - axis and what do they each represent?
2. what is the y - intercept of the graph? write a sentence describing what this represents.
3. what is the rate of change of the graph? write a sentence describing what this represents.
4. write a linear equation that models this relationship.
5. if britney has $360 in her coin bank, how many weeks has she been saving her money? show your work and answer with a sentence.
6. predict how much money britney would have in her coin bank if she saved for 14 weeks. show your work and answer with a sentence.

Explanation:

Step1: Identify the linear equation form

The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept. From the graph, we can see that when \( x = 0 \) (at week 0), \( y=20 \), so \( b = 20 \). To find the slope \( m \), we can use two points. Let's take \( (0,20) \) and \( (1,40) \). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the values, we get \( m=\frac{40 - 20}{1 - 0}=\frac{20}{1}=20 \).

Step2: Write the linear equation

Substitute \( m = 20 \) and \( b = 20 \) into the linear equation form \( y=mx + b \). So the equation is \( y = 20x+20 \), where \( x \) is the number of weeks and \( y \) is the amount of money in the coin bank.

Answer:

The linear equation that models this relationship is \( y = 20x + 20 \) (where \( x \) represents the number of weeks and \( y \) represents the amount of money in Britney's coin bank in dollars).