nterpreting Linear Relationships Quick Check

Question

3 of 53 of 5 Items
Question
Jane opened a savings account and deposited $200. Every month, she deposits another $100. Select the graph that shows how much money will be in her savings account over time.(1 point)
Responses

A coordinate graph shows the x-axis labeled as months ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 700 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 200 right parenthesis, left parenthesis 1 comma 300 right parenthesis, left parenthesis 2 comma 400 right parenthesis, and left parenthesis 3 comma 500 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as months ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 700 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 200 right parenthesis, left parenthesis 1 comma 300 right parenthesis, left parenthesis 2 comma 400 right parenthesis, and left parenthesis 3 comma 500 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as months ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 700 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 200 right parenthesis, left parenthesis 2 comma 300 right parenthesis, left parenthesis 4 comma 400 right parenthesis, and left parenthesis 6 comma 500 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as months ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 700 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 200 right parenthesis, left parenthesis 2 comma 300 right parenthesis, left parenthesis 4 comma 400 right parenthesis, and left parenthesis 6 comma 500 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as months ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 800 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 200 right parenthesis, left parenthesis 1 comma 400 right parenthesis, left parenthesis 2 comma 600 right parenthesis, and left parenthesis 3 comma 800 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as months ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 800 in increments of 100. Four unlabeled points are plotted as follows: left parenthesis 0 comma 200 right parenthesis, left parenthesis 1 comma 400 right parenthesis, left parenthesis 2 comma 600 right parenthesis, and left parenthesis 3 comma 800 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as months ranging from 0 to 10 in 1 unit increments and the y-axis labeled as dollars ranging from 0 to 700 in increments of 100. Three unlabeled points are plotted as follows: left parenthesis 0 comma 200 right parenthesis, left parenthesis 3 comma 400 right parenthesis, and left parenthesis 6 comma 600 right parenthesis. A solid arrow passes through these points.

Answer 1

To determine which graph correctly represents Jane's savings account over time, let's break down the situation based on the information provided:

1. Initial Deposit: Jane starts with an initial deposit of $200.
2. Monthly Deposit: Every month, she adds another $100 to her account.

This creates a linear relationship where:

• The starting amount is $200 (when \(x = 0\)).
• For every month (1 unit on the x-axis), her balance increases by $100.

To find the total amount in her savings account after \(x\) months, we can use the formula:

\[ \text{Total Amount} = 200 + 100x \]

Calculating Values:

• At month 0: \[ 200 + 100 \times 0 = 200 \]
• At month 1: \[ 200 + 100 \times 1 = 300 \]
• At month 2: \[ 200 + 100 \times 2 = 400 \]
• At month 3: \[ 200 + 100 \times 3 = 500 \]

From this, the points we expect to see on the graph are:

• (0, 200)
• (1, 300)
• (2, 400)
• (3, 500)

Finding the Correct Graph: Looking through the options you've provided:

• The first graph shows the points (0, 200), (1, 300), (2, 400), and (3, 500).
• The subsequent graphs do not correspond to the expected relationship since either they have incorrect amounts, skip months, or adjust inappropriately.

Thus, the correct graph that represents Jane's savings account over time is the first graph.