Question

Kim is trying to do a better job of managing her money. A book on personal finance recommends that she track how much she spends on different items. Kim knows she spends a lot on "nonessentials" such as buying a cup of coffee or buying small items from street vendors. She finds it hard to track these purchases so she decides to set aside a certain amount of money in cash that she will use for these purchases. Every Sunday, she records how much she has left. She keeps a record for 10 weeks. Her data are approximately linear so she made the following graph in which she extends the model past 10 weeks Amount left to spend ($) 600 500 400 300 200 100 0 0 Non-Essential Expenses S 15 10 Number of Weeks • Slope • Vertical intercept o Horizontal intercept 20 a. Complete the table below by matching the following mathematical terms to the appropriate contextual meaning and estimating the values from the graph. Contextual Meaning Amount Kim sets aside for non-essential items Time it takes Kim to spend the entire amount Amount Kim spends per week 25 Mathematical Term Vertical intercept ✓ Horizontal intercept Slope 500 20 Value (including units) ✓ dollars ✓ weeks dollars per week​

Answer 1

The vertical intercept is the amount Kim sets aside for non-essentials, estimated at 500 dollars. The horizontal intercept is the number of weeks it takes for her to spend this amount, around 20 weeks. The slope represents her weekly spending on non-essentials, calculated as 25 dollars per week.

Step-by-step explanation:

To match the mathematical terms to their contextual meanings and estimate values for Kim's situation with non-essential spending, we need to interpret the graphical data presented. The vertical intercept represents the initial amount of money Kim sets aside for non-essential items, which can be estimated from the graph. The horizontal intercept represents the time it takes for Kim to spend the entire amount on non-essentials. The slope of the line indicates the amount Kim spends per week on non-essentials.

• Vertical Intercept (Amount Kim sets aside for non-essential items): Approximately 500 dollars
• Horizontal Intercept (Time it takes Kim to spend the entire amount): Approximately 20 weeks
• Slope (Amount Kim spends per week): To calculate this, we can use two points on the line. If she starts with 500 dollars and in 10 weeks she has half left, she spends about 25 dollars per week (500 dollars / 20 weeks).