Question

mia has been babysitting all summer. she wants to save money to purchase tickets to a georgia bulldogs basketball game.

number of days, m	amount saved, d(m)
10	58
16	73
20	88

1. part a: assuming she saves the same amount of money each day, create an equation to represent the amount she will have saved, d(m), after any number of days, m.

which of the following statements is true?

this scenario can be represented by the function a) d(m)=5m + 43 where $5 was the initial amount saved and $43 was the amount saved per day.
this scenario can be represented by the function b) d(m)=3m + 28 where $28 was the initial amount saved and $3 was the amount saved per day.
this scenario can be represented by the function c) d(m)=3m + 28 where $3 was the initial amount saved and $28 was the amount saved per day.
this scenario can be represented by the function d) d(m)=5m + 43 where $43 was the initial amount saved and $5 was the amount saved per day.

Explanation:

Step1: Encontrar la pendiente (tasa de cambio)

La pendiente $m$ de una función lineal $y = mx + b$ se calcula como $\frac{\Delta y}{\Delta x}$. Aquí, $x$ es el número de días $m$ y $y$ es el monto ahorrado $d(m)$. Tomando dos puntos, por ejemplo, $(10,58)$ y $(15,73)$:
\[m=\frac{73 - 58}{15 - 10}=\frac{15}{5}=3\]

Step2: Encontrar el término independiente (valor inicial)

Usamos la ecuación de la recta $y=mx + b$ y un punto, digamos $(10,58)$. Sustituyendo $x = 10$, $y = 58$ y $m = 3$:
\[58=3\times10 + b\]
\[58 = 30 + b\]
\[b=58 - 30=28\]
La ecuación es $d(m)=3m + 28$, donde $28$ es el monto inicial ahorrado y $3$ es el monto ahorrado por día.

Answer:

B. $d(m)=3m + 28$ donde $\$28$ fue el monto inicial ahorrado y $\$3$ fue el monto ahorrado por día.