Question

The following equation represents the cost of buying a meal with one meat and options for the number of side dishes, x.
y=11+1.25x

What is the y-intercept?
What does the y-intercept mean in context?
What is the slope?
What does the slope mean in context?
If Jodi paid $18.50 for her meal, how many side dishes did she get?

Answer 1

To analyze the equation \( y = 11 + 1.25x \), where \( y \) is the total cost of the meal and \( x \) is the number of side dishes, we can find the following:

### 1. Y-intercept
The y-intercept can be found by examining the equation when \( x = 0 \):
\[
y = 11 + 1.25(0) = 11
\]

### 2. Meaning of the y-intercept in context
The y-intercept represents the total cost of a meal that includes one meat and no side dishes. In this case, if Jodi ordered just one meat without any side dishes, her total cost would be $11.

### 3. Slope
The slope of the equation is the coefficient of \( x \), which is \( 1.25 \).

### 4. Meaning of the slope in context
The slope indicates the additional cost for each side dish ordered. Specifically, for each side dish \( x \) that Jodi orders, the total cost of her meal increases by $1.25.

### 5. Finding the number of side dishes Jodi got
If Jodi paid $18.50 for her meal, we can set \( y \) equal to $18.50 and solve for \( x \):
\[
18.50 = 11 + 1.25x
\]
First, subtract 11 from both sides:
\[
18.50 - 11 = 1.25x \implies 7.50 = 1.25x
\]
Next, divide both sides by 1.25 to find \( x \):
\[
x = \frac{7.50}{1.25} = 6
\]

### Conclusion
Jodi got **6 side dishes** with her meal.