Respuesta :
Answer:
An equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;
[tex]y=50x+100[/tex]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.
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;
[tex]y=mx+b[/tex]After 3 weeks, the bank account contained $250;
[tex]\begin{gathered} 250=m(3)+b \\ 3m+b=250 \end{gathered}[/tex]After 10 weeks the bank account contained $600;
[tex]\begin{gathered} 600=m(10)+b \\ 10m+b=600 \end{gathered}[/tex]Solving for m and b;
subtract the first equation from the second.
[tex]\begin{gathered} 10m-3m+b-b=600-250 \\ 7m=350 \\ m=\frac{350}{7} \\ m=50 \end{gathered}[/tex]substituting the value of m into the first equation;
[tex]\begin{gathered} 3m+b=250 \\ 3(50)+b=250 \\ 150+b=250 \\ b=250-150 \\ b=100 \end{gathered}[/tex]Therefore, an equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;
[tex]y=50x+100[/tex]From the equation above, the slope m of the equation is;
[tex]m=50[/tex]and the y-intercept b of the equation is;
[tex]b=100[/tex]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.
