Question

graphs and functions interpreting the parameters of a linear function that models a real - world... sam is putting money into a checking account. let y represent the total amount of money in the account (in dollars). let x represent the number of weeks sam has been adding money. suppose that x and y are related by the equation 750 + 20x = y. answer the questions below. note that a change can be an increase or a decrease. for an increase, use a positive number. for a decrease, use a negative number. (a) what is the change per week in the amount of money in the account? $\square$ (b) what was the starting amount of money in the account? $\square$

Explanation:

Step1: Identify the linear equation form

The given equation is \( y = 20x + 750 \), which is in the slope - intercept form \( y=mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value).

Step2: Find the change per week (slope)

In the equation \( y = 20x+750 \), the coefficient of \( x \) is 20. This represents the change in \( y \) (amount of money in the account) for a unit change in \( x \) (number of weeks). Since \( x \) is the number of weeks, the change per week is 20. And since the amount of money is increasing as the number of weeks increases, we use a positive number.

Step3: Find the starting amount (y - intercept)

In the equation \( y = 20x + 750 \), when \( x = 0 \) (at week 0, the starting time), \( y=750 \). So the starting amount of money in the account is 750.

Answer:

(a) The change per week in the amount of money in the account is \(\$20\).
(b) The starting amount of money in the account is \(\$750\).