Let’s solve each problem step by step, interpreting the slope and y-intercept in context.
---
Problem 1: Hamburger Cost Function
Function:
f(t) = 1.90 + 1.40t
This is a linear function where:
- `t` = number of toppings
- `f(t)` = total cost of the hamburger (in dollars)
---
####
a. What is the y-intercept, and what does it mean?
In the equation `f(t) = 1.90 + 1.40t`, the
y-intercept is the constant term:
1.90
>
Meaning: When `t = 0` (no toppings), the cost of the hamburger is $1.90.
> So, the y-intercept represents the
base cost of the hamburger with no toppings.
✔ Answer: The y-intercept is
1.90, and it means the cost of a hamburger with
0 toppings is
$1.90.
---
####
b. What is the slope, and what does it mean?
The
slope is the coefficient of `t`:
1.40
>
Meaning: For each additional topping (`t` increases by 1), the cost increases by $1.40.
> So, the slope represents the
cost per topping.
✔ Answer: The slope is
1.40, and it means
each topping costs $1.40.
---
####
c. If Jodi paid $3.30 for a hamburger, how many toppings were on Jodi’s hamburger?
We are given:
f(t) = 3.30
Set up the equation:
```
1.90 + 1.40t = 3.30
```
Subtract 1.90 from both sides:
```
1.40t = 3.30 - 1.90
1.40t = 1.40
```
Divide both sides by 1.40:
```
t = 1.40 / 1.40
t = 1
```
✔ Answer: Jodi’s hamburger had
1 topping.
---
Problem 2: Ice Cream Sundae Cost Function
Function:
f(t) = 2.25 + 0.75t
Where:
- `t` = number of toppings
- `f(t)` = total cost of the sundae (in dollars)
---
####
a. What is the y-intercept, and what does it mean?
The
y-intercept is
2.25
>
Meaning: When `t = 0` (no toppings), the cost is $2.25.
> So, this is the
base cost of the sundae with no toppings.
✔ Answer: The y-intercept is
2.25, and it means the cost of a sundae with
0 toppings is
$2.25.
---
####
b. What is the slope, and what does it mean?
The
slope is
0.75
>
Meaning: For each additional topping, the cost increases by $0.75.
> So, the slope represents the
cost per topping.
✔ Answer: The slope is
0.75, and it means
each topping costs $0.75.
---
####
c. If Kaye paid $6.00 for a sundae, how many toppings were on Kaye’s sundae?
Given:
f(t) = 6.00
Set up the equation:
```
2.25 + 0.75t = 6.00
```
Subtract 2.25 from both sides:
```
0.75t = 6.00 - 2.25
0.75t = 3.75
```
Divide both sides by 0.75:
```
t = 3.75 / 0.75
t = 5
```
✔ Answer: Kaye’s sundae had
5 toppings.
---
##
✔ Final Answers Summary:
Problem 1: Hamburger
a. Y-intercept =
1.90 → base cost with 0 toppings
b. Slope =
1.40 → each topping costs $1.40
c. Toppings =
1
Problem 2: Sundae
a. Y-intercept =
2.25 → base cost with 0 toppings
b. Slope =
0.75 → each topping costs $0.75
c. Toppings =
5
Let me know if you’d like to graph these or explore more examples!
Parent Tip: Review the logic above to help your child master the concept of interpreting slope and y intercept worksheet.
