Math Problem Statement
Carmen opens a savings account after starting her summer job and deposits money into it each month. The graph represents the relationship between y , the total amount of money in her account, and x the number of months since she began saving. Which equation best represents the relationship between x and y ? A.y=−50+100
B.y=100x+50
C.y=50x+100
D.y=100x−50
Solution
To find the correct equation that represents the relationship between (months) and (money saved), we can interpret the graph step by step.
Observations from the graph:
-
Initial value (y-intercept): At (when no months have passed), the amount of money saved is $50. This means that the y-intercept is 50.
-
Rate of saving (slope): The graph shows a consistent, linear increase in the amount of money saved over time. From month 1 to month 2, the amount saved increases from $150 to $250, which gives a change in of $100 over a change in of 1 month. This indicates that Carmen saves $100 per month, which gives a slope of 100.
The equation of a line is given by:
Where is the slope and is the y-intercept.
Substituting the values:
- Slope
- Y-intercept
So the equation becomes:
Therefore, the correct answer is B. .
Let me know if you want more details or have any questions!
Here are some related questions:
- How would the graph change if Carmen saved more money per month?
- What would the equation look like if the initial savings were $0?
- How would the slope change if the savings rate doubled?
- How can you calculate the total money saved after 6 months using the equation?
- What other factors could influence the shape of the savings graph over time?
Tip: The slope of a graph shows the rate of change—here, it represents how much money Carmen saves per month.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graph Interpretation
Formulas
y = mx + b
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 7-9
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