Question

the table shows the amount of money, a, in a savings account after n months. select all the equations that represent the relationship between the amount of money, a, and the number of months, n.

number of months	dollar amount
6	1,300
7	1,400
8	1,500

a. a = 100n
b. a = 100(n - 5)
c. a - 700 = 100n
d. a - 1,200 = 100n
e. a = 700 + 100n
f. a = 1200 + 100n
g. a = 1,200 + 100(n - 5)

Explanation:

Step1: Find the rate of change

The change in amount $\Delta A=1300 - 1200=100$ when the change in months $\Delta m = 6 - 5=1$. The rate of change (slope) is $\frac{\Delta A}{\Delta m}=100$.

Step2: Use the point - slope form

We can use the point - slope form of a linear equation $y - y_1=m(x - x_1)$. Using the point $(m_1,A_1)=(5,1200)$ and slope $m = 100$, we get $A-1200 = 100(m - 5)$. Simplifying gives $A=1200+100(m - 5)$.
We can also find the $y$-intercept form. Let $A=bm + c$. Substituting $m = 5,A = 1200$ and $b = 100$ into $A=bm + c$, we have $1200=100\times5 + c$. Solving for $c$: $c=1200 - 500=700$. So the equation is $A=700 + 100m$.

Answer:

E. $A = 700+100m$, G. $A = 1200+100(m - 5)$