Question

jack starts with 2 dollars in his account. he deposits the same amount of money each day. this graph represents the relationship between the number of days and the amount in the bank account. use the slope and vertical intercept to write an equation. vertical intercept = 2

Explanation:

Step1: Identify the linear equation form

The general form of a linear equation is \( y = mx + b \), where \( y \) is the dependent variable, \( m \) is the slope, \( x \) is the independent variable, and \( b \) is the y - intercept. In this context, the "dollars in account" (let's call this \( y \)) depends on the "number of days" (let's call this \( x \)), the "amount deposited per day" is the slope (\( m \)), and the "starting amount" is the y - intercept (\( b = 2 \)).

Step2: Determine the slope

We know two points on the line. When \( x = 0 \), \( y = 2 \) (the starting point). When \( x = 1 \), from the graph, \( y = 10 \)? Wait, no, looking at the graph, when \( x = 0 \), \( y = 2 \); when \( x = 1 \), \( y = 10 \)? Wait, no, the grid: from \( (0,2) \) to \( (1,10) \)? Wait, no, the y - axis: at \( x = 0 \), \( y = 2 \); at \( x = 1 \), let's count the grid. The vertical axis is dollars, with each grid line (small square) probably 2? Wait, no, the first point after \( (0,2) \): when \( x = 0.5 \), maybe? Wait, no, the problem says "deposits the same amount each day". The starting amount is 2 (when \( x = 0 \)). Let's find two clear points. At \( x = 0 \), \( y = 2 \); at \( x = 2 \), \( y = 18 \)? Wait, no, the graph: the line goes from \( (0,2) \) up. Wait, maybe the slope is calculated as \( \frac{\Delta y}{\Delta x} \). Let's take \( x = 0 \), \( y = 2 \) and \( x = 1 \), \( y = 10 \)? Wait, no, the vertical intercept is 2. Let's see the labels: "dollars in account" is the total, "starting amount" is 2, "amount deposited per day" is the slope, "number of days" is \( x \).

The equation should be: dollars in account = (amount deposited per day) * (number of days) + starting amount.

From the graph, when \( x = 0 \), dollars in account = 2 (starting amount). When \( x = 1 \), let's see the graph: at \( x = 1 \), the y - value is 10? Wait, no, the grid: the first square above 2 is 4, then 6, 8, 10 at \( x = 1 \)? Wait, no, the line passes through (0,2) and (1,10)? Wait, the slope would be \( \frac{10 - 2}{1 - 0}=8 \)? Wait, but maybe the slope is 8? Wait, but the labels: the equation structure is dollars in account = (amount deposited per day) * (number of days) + starting amount.

So the left - hand side is "dollars in account", then we have (amount deposited per day) multiplied by (number of days) plus (starting amount).

So filling in the boxes:

First box (left - most): dollars in account

Second box: amount deposited per day

Third box: number of days

Fourth box: starting amount? Wait, no, the equation is \( y=mx + b \), where \( y \) is dollars in account, \( m \) is amount deposited per day, \( x \) is number of days, and \( b \) is starting amount. So the equation is: dollars in account = (amount deposited per day) * (number of days) + starting amount.

Let's check with \( x = 0 \): dollars in account = (amount deposited per day)*0 + starting amount = starting amount = 2, which matches.

When \( x = 1 \), if amount deposited per day is 8 (since from \( x = 0 \) to \( x = 1 \), dollars go from 2 to 10? Wait, no, the graph: at \( x = 1 \), the y - value is 10? Wait, the vertical axis: 2, 4, 6, 8, 10 at \( x = 1 \). So the slope (amount per day) is \( 10 - 2=8 \) when \( x = 1 \). So the equation is dollars in account = (amount deposited per day) * number of days + starting amount.

So the boxes:

First box: dollars in account

Second box: amount deposited per day

Third box: number of days

Fourth box: starting amount

Wait, the structure is: [dollars in account] = [amount deposited per day] * [number of days] + [starting amount]

Let's confirm the labels:

- "dollars in account" is the total, so left - hand side.

- "amount deposited per day" is the rate (slope), multiplied by "number of days" (x), and then add "starting amount" (y - intercept, 2).

So the filling:

First box: dollars in account

Second box: amount deposited per day

Third box: number of days

Fourth box: starting amount

Answer:

dollars in account = amount deposited per day × number of days + starting amount

(So in the boxes: first box: dollars in account; second box: amount deposited per day; third box: number of days; fourth box: starting amount)