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

Question

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

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 2

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 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!