Question

1. sarah makes a monthly payment of $120 for her gym membership. using the table below, interpret the function that describes the amount of money left in sarahs savings account after each payment.

is this a linear line? yes no
does the line increase or decrease?

Explanation:

Step1: Check if it's a linear line

Calculate the change in savings balance each month.
From month 1 to 2: \(760 - 880=- 120\)
From month 2 to 3: \(640 - 760=-120\)
Since the change is constant (\(-120\) each month), it is a linear line.

Step2: Determine if it increases or decreases

Since the change (\(-120\)) is negative, the line decreases.

Step3: Interpret the function

Let \(x\) be the number of months and \(y\) be the savings balance.
The initial amount (when \(x = 0\)): Let's use the point - slope form \(y-y_1=m(x - x_1)\). Using the point \((1,880)\) and \(m=-120\)
\(y-880=-120(x - 1)\)
\(y-880=-120x + 120\)
\(y=-120x+1000\)
The function \(y=-120x + 1000\) (where \(x\) is the number of months and \(y\) is the savings balance) means that Sarah starts with \(\$1000\) in her savings account and each month (\(x\) increases by 1) she pays \(\$120\) (so her savings \(y\) decreases by 120) for her gym membership.

Answer:

Is this a linear line? Yes
Does the line increase or decrease? Decrease
The function \(y=-120x + 1000\) (where \(x\) is the number of months and \(y\) is the savings balance) means Sarah starts with \(\$1000\) and pays \(\$120\) per month for gym membership.