Question

miguel saves the same amount of money into a bank account each week. the bank account started with some money in it. after 3 weeks, the bank account contained $250. after 10 weeks the bank account contained $600.write an equation that cqn be used to model tbe number of dollars, y,iguel saves in x weeks.exain what slope and y intercept of youre equation mean in the context of the aituation.enter your equation and your explanations in tbe space provided.

Answer 1

An equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;

`y=50x+100`

The slope of the equation in the context is the amount of money Miguel saves in the bank account each week. So, Miguel saves $50 each week.

The y-intercept of the equation in the context is the amount of money Miguel initially have in the bank account. So, the initial amount of money in the bank account is $100.

Step-by-step explanation:

Given that Miguel saves the same amount of money into a bank account each week.

Let y represent the amount of money in the account after x weeks;

`y=mx+b`

After 3 weeks, the bank account contained $250;

`\begin{gathered} 250=m(3)+b \\ 3m+b=250 \end{gathered}`

After 10 weeks the bank account contained $600;

`\begin{gathered} 600=m(10)+b \\ 10m+b=600 \end{gathered}`

Solving for m and b;

subtract the first equation from the second.

`\begin{gathered} 10m-3m+b-b=600-250 \\ 7m=350 \\ m=(350)/(7) \\ m=50 \end{gathered}`

substituting the value of m into the first equation;

`\begin{gathered} 3m+b=250 \\ 3(50)+b=250 \\ 150+b=250 \\ b=250-150 \\ b=100 \end{gathered}`

Therefore, an equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;

`y=50x+100`

From the equation above, the slope m of the equation is;

`m=50`

and the y-intercept b of the equation is;

`b=100`

The slope of the equation in the context is the amount of money Miguel saves in the bank account each week. So, Miguel saves $50 each week.

The y-intercept of the equation in the context is the amount of money Miguel initially have in the bank account. So, the initial amount of money in the bank account is $100.