Math Problem Statement

Elijah only deposits money in his bank account each week. After saving a certain amount of money, no money is deposited or withdrawn from the account for some time. Then, he uses the money in the account to pay back a friend a little bit each week. This graph shows the amount of money as a function of time in weeks. What is the slope of this highlighted line segment? x y 0 1 2 3 4 5 6 7 8 9 10 0 20 40 60 80 100 120 140 160 180 200 Time (weeks) Amount of money in the bank The slope is . Great job! You just found that the slope of this highlighted line segment is 40. What does the slope of 40 mean in this situation? x y 0 1 2 3 4 5 6 7 8 9 10 0 20 40 60 80 100 120 140 160 180 200 Time (weeks) Amount of money in the bank The slope is 40.

Every 40 weeks, the amount of money in the bank increases by $1.

The amount of money in the bank increases at a rate of $40 per week.

There is a total of $40 in the bank. Great job! What is the slope of this highlighted line segment? x y 0 1 2 3 4 5 6 7 8 9 10 0 20 40 60 80 100 120 140 160 180 200 Time (weeks) Amount of money in the bank The slope is .

Solution

It seems you're asking for the slope of the highlighted line segment on a graph of the amount of money in a bank account over time. From your description, the graph is plotting "time in weeks" on the x-axis and "amount of money in the bank" on the y-axis.

To find the slope of the line, we need to determine the "rise" (change in the amount of money) over the "run" (change in time). This is given by the formula for slope:

slope=change in ychange in x=ΔyΔx\text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{\Delta y}{\Delta x}

You mentioned that the slope is 40, and you also described the situation as the amount of money increasing at a rate of $40 per week.

So, the slope of 40 means:

The amount of money in the bank increases at a rate of $40 per week.


Would you like further explanation on calculating slopes, or would you like to explore other related concepts? Here's a set of questions that could help:

  1. How do you calculate the slope from two points on a line?
  2. How can you interpret the slope in real-world situations beyond banking?
  3. What does a slope of zero represent in a graph of savings?
  4. How would the slope change if the money started decreasing over time instead of increasing?
  5. Can the slope of a graph be negative, and what would that represent in this case?

Tip: When you interpret a slope, always ask yourself, "What is changing in the y-direction (vertical) and what is changing in the x-direction (horizontal)?"

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Math Problem Analysis

Mathematical Concepts

Slope
Rate of Change
Linear Relationships

Formulas

Slope formula: slope = Δy / Δx

Theorems

Concept of slope as a measure of rate of change in linear functions

Suitable Grade Level

Grades 6-8