Question

The function below shows the cost of a hamburger with different numbers of toppings (t).
f(t) = 1.90 + 1.40t

a. What is the y-intercept, and what does it mean?


b. What is the slope, and what does it mean?


c. If Jodi paid $3.30 for a hamburger, how many toppings were on Jodi’s hamburger?

Answer 1

Let's analyze the function \( f(t) = 1.90 + 1.40t \) step by step.

### a. Y-Intercept
The y-intercept of a function is the value of the function when the input (in this case, the number of toppings \( t \)) is zero.

For \( f(t) = 1.90 + 1.40t \):

- When \( t = 0 \):
\[
f(0) = 1.90 + 1.40(0) = 1.90
\]

**Interpretation of the y-intercept:**
The y-intercept \( 1.90 \) represents the cost of a hamburger with no toppings. So, the base price of the hamburger itself is $1.90.

---

### b. Slope
The slope of the function indicates how much the function value (cost of the hamburger) increases for each additional topping.

In the function \( f(t) = 1.90 + 1.40t \), the slope is \( 1.40 \).

**Interpretation of the slope:**
The slope \( 1.40 \) means that for each additional topping added to the hamburger, the cost increases by $1.40.

---

### c. Finding the Number of Toppings
To find the number of toppings \( t \) on Jodi's hamburger when she paid $3.30, we can set the function equal to 3.30 and solve for \( t \):

\[
f(t) = 3.30
\]

Substituting the function into the equation gives:

\[
1.90 + 1.40t = 3.30
\]

Now, we can solve for \( t \):

1. Subtract \( 1.90 \) from both sides:
\[
1.40t = 3.30 - 1.90
\]
\[
1.40t = 1.40
\]

2. Divide both sides by \( 1.40 \):
\[
t = \frac{1.40}{1.40} = 1
\]

**Conclusion:**
Jodi had \( 1 \) topping on her hamburger.