You're absolutely right —
Connor will run out of money first.
Let’s break this down step by step to understand why, using both the graph and the math.
---
📌 Given:
-
Connor: Started with $600, spends $20/month →
negative slope = -20
-
Carlie: Started with $500, spends $10/month →
negative slope = -10
We’re modeling their savings over time as linear equations in
slope-intercept form:
>
y = mx + b
Where:
- `y` = amount of money left
- `x` = number of months
- `m` = rate of change (spending per month → negative)
- `b` = starting amount (y-intercept)
---
✏️ Write the equations:
Connor:
> y = -20x + 600
Carlie:
> y = -10x + 500
---
⏳ When do they run out of money?
They run out of money when
y = 0 (no money left).
#### ➤ For Connor:
Set y = 0:
> 0 = -20x + 600
> 20x = 600
>
x = 30 months
#### ➤ For Carlie:
Set y = 0:
> 0 = -10x + 500
> 10x = 500
>
x = 50 months
---
📊 Graph Interpretation:
On the graph:
- The
x-axis is months.
- The
y-axis is dollars.
- Each line hits the x-axis (where y=0) at the point where money runs out.
→ Connor’s line (steeper, orange) hits x-axis at
x=30.
→ Carlie’s line (less steep, purple) hits x-axis at
x=50.
So visually, Connor’s line crosses the x-axis
first, meaning he runs out of money sooner.
---
💡 Why does this happen?
Even though Connor started with
more money ($600 vs $500), he spends
twice as fast ($20/month vs $10/month). His steeper downward slope means his money depletes faster.
---
✔ Final Answer:
>
Connor will run out of money first — after 30 months.
Carlie will last 50 months, so she runs out later.
---
Great job on your handwritten work — you correctly identified the equations and the answer! 👏
Parent Tip: Review the logic above to help your child master the concept of interpreting graphs of functions worksheet.
