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

A. What is the y-intercept?

B. What does the y-intercept mean in context?

C. What is the slope?

D. What does the slope mean in context?

E. If Jodi paid $18.50 for her meal, how many side dishes did she get?

Answer 1

their is (0,11)

also some other options for D is

the cost of a meal with 0 sides

the number of side dishes per cost

the number of sides that would cost you $0

if the correct one

Answer 2

Let's break down the equation \( y = 11 + 1.25x \), where \( y \) represents the total cost of the meal, and \( x \) represents the number of side dishes.

### A. What is the y-intercept?
The y-intercept of an equation in the form \( y = mx + b \) is the value of \( y \) when \( x = 0 \). In this equation, when \( x = 0 \):
\[
y = 11 + 1.25(0) = 11
\]
So, **the y-intercept is 11**.

### B. What does the y-intercept mean in context?
In the context of the meal, the y-intercept of 11 means that if Jodi chooses no side dishes (i.e., \( x = 0 \)), the cost of her meal would be $11. This value represents the base cost of the meal with just one meat.

### C. What is the slope?
The slope of the equation \( y = 11 + 1.25x \) is the coefficient of \( x \). Here, the slope is \( 1.25 \). So, **the slope is 1.25**.

### D. What does the slope mean in context?
In this context, the slope of 1.25 means that for each additional side dish Jodi chooses (for each increase of 1 in \( x \)), the total cost of her meal increases by $1.25.

### E. If Jodi paid $18.50 for her meal, how many side dishes did she get?
To find out how many side dishes \( x \) Jodi had, we can set the equation equal to 18.50 and solve for \( x \):
\[
18.50 = 11 + 1.25x
\]
Subtract 11 from both sides:
\[
18.50 - 11 = 1.25x
\]
\[
7.50 = 1.25x
\]
Now, divide both sides by 1.25:
\[
x = \frac{7.50}{1.25} = 6
\]
So, **Jodi had 6 side dishes**.

Answer 3

Thank you for your follow-up! Let's clarify the context for the slope in option D more thoroughly.

### D. What does the slope mean in context?
Given the options you provided, we can reflect on them and determine the most accurate interpretation of the slope \( 1.25 \):

1. **The cost of a meal with 0 sides**: This describes the y-intercept, which is $11 (when \( x = 0 \)).

2. **The number of side dishes per cost**: This is somewhat unclear; it may imply a rate of change, but it's not a standard interpretation of slope in this context.

3. **The number of sides that would cost you $0**: This is not correct in this context; the slope describes additional costs related to side dishes, not the number corresponding to a $0 cost.

The best interpretation from the provided options would be **"the cost of a meal with 0 sides"** since the y-intercept indicates the cost without any side dishes. However, we should clarify:

- The slope (which is 1.25) represents the **additional cost for each side dish** added to the meal, which means the total cost increases by $1.25 for each side dish ordered.

So, the best contextual meaning of the slope would be that for each additional side dish ordered, the meal's total cost increases by $1.25, rather than "the cost of a meal," which directly refers to the y-intercept.

Please let me know if you would like to delve deeper into any specific aspect!