Problem 88 - Algebra 1

Question

the table shows estimated costs of raising a child born in 1996 to a low income family for the child’s first seven years. $$ \begin{array}{|l|l|l|l|l|l|l|l|} \hline \text { Tere } & 1996 & 1997 & 1998 & 1999 & 2000 & 2001 & 2002 \\ \hline \text { Comporesitos } & 5670 & 5960 & 6280 & 6730 & 7080 & 7450 & 8000 \\\ \hline \end{array} $$ Make a line graph of the data.

Step-by-Step Solution

Answer

The line graph would start at (1996, 5670) and end at (2002, 8000), with points at each given year connected by straight lines to show the increase in the estimated cost of raising a child over these years.

Step 1: Understand the data in the table

Looking at the table, note that the first row indicates the year ('Tere') from 1996 to 2002. The second row under 'Comporesitos' represents the estimated costs of raising a child for each corresponding year.

Step 2: Define the coordinates for the graph

For the graph, we use the years for our x-coordinates and the corresponding costs for our y-coordinates. The pair (1996, 5670) would be our first coordinate for instance.

Step 3: Plot the data on a graph

First, draw axes on your graph. Label the horizontal x-axis as 'Year' and the vertical y-axis as 'Estimated Cost'. Remember to mark the scales. You can represent the years 1996-2002 on the x-axis, and the costs from 5670 to 8000 on the y-axis. Then plot each pair from our data on the graph as points.

Step 4: Draw the line graph

After you have plotted all the points, connect them with straight lines from one point to the next (1996 to 1997, 1997 to 1998, and so on). This line will illustrate the overall trend of the rising cost.

Key Concepts

Data Interpretation

When faced with numerical data, the first step is to extract meaningful insights. Observing our table, we need to focus on two key elements: the years and the estimated costs associated with each year. Each year from 1996 to 2002 has a corresponding cost, indicating the expense of raising a child in a low-income family for that particular year. These numbers can seem arbitrary at first. However, with the correct interpretation, they tell the story of increasing financial demands over time.

To properly interpret this data:

• Examine patterns or trends within the years.
• Note any relationships or fluctuations between consecutive years.
• Understand any potential reasons for increases, such as inflation or changes in living standards.

Once you grasp these insights, the data transitions from static numbers to a narrative about socio-economic factors affecting families.

Graphing Coordinates

A cornerstone of understanding line graphs is grasping how to plot data points using coordinates. For our exercise, each year and its corresponding cost form a pair that is a coordinate in a two-dimensional space, perfect for a line graph.

Here's how you can approach graphing them:

• On the x-axis, list the years from 1996 to 2002. Each section should evenly distribute to allow easy marking.
• On the y-axis, list estimated costs starting at 5670 up to 8000. Choose a scale that easily fits all numbers.
• Plot each year's cost as a point in the graph, based on its coordinate. For instance, the pair (1996, 5670) represents a point where the line for 1996 meets the line for 5670.

Connecting these coordinates will form the foundational structure of the graph, allowing for effective visualization of the data over time.

Trend Analysis

Understanding the trend is vital in comprehending the bigger picture that data offers. Once you've plotted all data points and connected them with lines, you can start observing the overall pattern.

Here are the steps to analyze trends effectively:

• Look for any continuous rise or fall in the line. The slope of the line indicates the rate of change.
• Identify any periods where the trend changes, accelerates, or decelerates.
• Consider possible causes for these trends, such as economic shifts impacting family expenses.

In our graph, the trend shows an upward slope, indicating an increase in costs each year. This consistent rise reflects underlying economic conditions, such as inflation or increased living expenses, affecting low-income families. Recognizing these trends helps to predict future outcomes and inform decision-making.