Question

debra 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 debra has been adding money. suppose that x and y are related by the equation 30x + 550 = 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?
$
(b) what was the starting amount of money in the account?
$

Explanation:

Part (a)

Step1: Identify the slope-intercept form

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept (initial value). The given equation is \(y=30x + 550\).

Step2: Determine the change per week

In the context of this problem, \(x\) represents the number of weeks and \(y\) represents the total amount of money. The coefficient of \(x\) (the slope \(m\)) represents the change in \(y\) (amount of money) per unit change in \(x\) (per week). Here, the coefficient of \(x\) is \(30\). Since it is a positive number, it represents an increase. So the change per week in the amount of money in the account is \(30\) dollars per week.

Part (b)

Step1: Recall the slope - intercept form

The equation \(y = mx + b\) has \(b\) as the initial value (the value of \(y\) when \(x = 0\)). In the equation \(y=30x + 550\), when \(x = 0\) (which means \(0\) weeks have passed), \(y=550\).

Step2: Interpret the initial value

When \(x = 0\) (at the start, before any weeks have passed), the amount of money in the account is given by the y - intercept. So the starting amount of money in the account is \(550\) dollars.

Part (a) Answer: \(30\)

Part (b) Answer: \(550\)

Answer:

Step1: Recall the slope - intercept form

The equation \(y = mx + b\) has \(b\) as the initial value (the value of \(y\) when \(x = 0\)). In the equation \(y=30x + 550\), when \(x = 0\) (which means \(0\) weeks have passed), \(y=550\).

Step2: Interpret the initial value

When \(x = 0\) (at the start, before any weeks have passed), the amount of money in the account is given by the y - intercept. So the starting amount of money in the account is \(550\) dollars.

Part (a) Answer: \(30\)

Part (b) Answer: \(550\)