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

Question

y = 11 + 1.25x

(5 points)
A.  What is the y-intercept?   (Response area)

B.  What does the y-intercept mean in context?   (Response area)

C.  What is the slope?  (Response area)

D.  What does the slope mean in context?  (Response area)

E.  If Jodi paid $18.50 for her meal, how many side dishes did she get?  (response area)
responses 
the cost of a meal with 0 sides 
(0, 1.25)
6
4
(11, 0)
5
1.25
the number of side dishes per cost 
7
(0,11)
the amount per side dish
the number of sides that would cost you 0$
11

GPT-4o mini · Answer

Let’s break down each part of the question regarding the equation $ y = 11 + 1.25x $:

A. What is the y-intercept?

The y-intercept is the value of $ y $ when $ x = 0 $. From the equation: \[ y = 11 + 1.25(0) \] So, the y-intercept is $ 11 $.

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

The y-intercept, $ 11 $, represents the cost of a meal with one meat and no side dishes (i.e., when $ x = 0 $). In context, this means that the base cost of the meal is $11.

C. What is the slope?

The slope of the equation $ y = 11 + 1.25x $ is the coefficient of $ x $, which is $ 1.25 $.

D. What does the slope mean in context?

The slope, $ 1.25 $, indicates the additional cost for each side dish added to the meal. In context, it means that for every side dish Jodi adds, 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 the number of side dishes Jodi got, we can set $ y = 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.

Summary of Answers

A: $ 11 $
B: The cost of a meal with 0 sides.
C: $ 1.25 $
D: The amount per side dish.
E: $ 6 $.

BTS ARMY · Answer

the graph has a straight going across from 100 to 10
Use the graph to check 4 statements that are true.

(4 points)
Responses

The graph is nonlinear.
The graph is nonlinear.

The graph is increasing at a constant rate of change.
The graph is increasing at a constant rate of change.

The graph is decreasing with a constant rate of change.
The graph is decreasing with a constant rate of change.

The slope of the graph shows a decrease of $100 each week.
The slope of the graph shows a decrease of $100 each week.

The slope of the graph has a length of 100.
The slope of the graph has a length of 100.

The slope of the graph shows a decrease of $100 in a 10 week period of time.
The slope of the graph shows a decrease of $100 in a 10 week period of time.

The graph is Linear.
The graph is Linear.

The slope of the graph shows that as the weeks increase, the loan also increases.
The slope of the graph shows that as the weeks increase, the loan also increases.

The graph is decreasing, but the rate of change does not stay constant.
The graph is decreasing, but the rate of change does not stay constant.

The y-intercept is (0, 1000) and shows that at 0 time, your loan is $1000
The y-intercept is (0, 1000) and shows that at 0 time, your loan is $1000

The x-intercept is (10, 0) and states that at 0 time, your loan is $10

GPT-4o mini · Answer

To assess the statements about the graph you described (a straight line going from 100 to 10), we’ll analyze the nature of the graph and its properties. Assuming that the graph represents the relationship of a loan decreasing over a period of time (in this case, from $1000 to $100 in 10 weeks), here are the correct evaluations for the statements provided:

The graph is nonlinear.
- False. The graph is linear because it is described as a straight line.
The graph is increasing at a constant rate of change.
- False. The graph is decreasing, not increasing.
The graph is decreasing with a constant rate of change.
- True. A straight line implies that the graph decreases with a constant rate of change.
The slope of the graph shows a decrease of $100 each week.
- False. If the graph decreases from $1000 to $100 over 10 weeks, the decrease per week is $ \frac{1000 - 100}{10} = 90 $, not $100.
The slope of the graph has a length of 100.
- False. The slope represents the rate of change (rise over run) rather than a "length."
The slope of the graph shows a decrease of $100 in a 10 week period of time.
- False. Same reasoning as above; the total decrease over 10 weeks would be $900.
The graph is Linear.
- True. The graph is linear since it is a straight line.
The slope of the graph shows that as the weeks increase, the loan also increases.
- False. As time increases, the loan decreases.
The graph is decreasing, but the rate of change does not stay constant.
- False. The rate of change is constant because it is a straight line.
The y-intercept is (0, 1000) and shows that at 0 time, your loan is $1000.
- True. This implies that at week 0, the loan amount is $1000.
The x-intercept is (10, 0) and states that at 0 time, your loan is $10.
- False. The x-intercept indicates that at week 10, the loan is $0, not $10.

Summary of True Statements

Based on the above analysis, the true statements are:

The graph is decreasing with a constant rate of change.
The graph is Linear.
The y-intercept is (0, 1000) and shows that at 0 time, your loan is $1000.

BTS ARMY · Answer

find one more answer

GPT-4o mini · Answer

Of course! Let's recap and analyze the statements again to identify an additional true statement based on the previous evaluations.

True Statements So Far

The graph is decreasing with a constant rate of change.
The graph is Linear.
The y-intercept is (0, 1000) and shows that at 0 time, your loan is $1000.

Additional Analysis

The graph's x-intercept at week 10 shows that the loan balance reaches $0. This means that it can be inferred that the loan is completely paid off after 10 weeks.

Additional True Statement

The x-intercept is (10, 0) and indicates the time when the loan balance reaches $0.

Given this clarification, the true statements associated with the graph now include this additional one!

Final List of True Statements

The graph is decreasing with a constant rate of change.
The graph is Linear.
The y-intercept is (0, 1000) and shows that at 0 time, your loan is $1000.
The x-intercept is (10, 0) and indicates the time when the loan balance reaches $0.

This gives you the required four true statements about the graph!

BTS ARMY · Answer

does the graph have the steepest slope, has the largest y-intercept, shows a decreasing relationship, or has a solution: after 3 blocks of time, you have 8$ x f(x) 0 2 1 4 2 6 3 8 4 10

GPT-4o mini · Answer

Let's analyze the information you've provided about the graph with the following data points:

\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline 0 & 2 \ 1 & 4 \ 2 & 6 \ 3 & 8 \ 4 & 10 \ \hline \end{array} \]

Analysis of Each Statement

Does the graph have the steepest slope?
- The slope between any two consecutive points can be calculated. The slope is constant in this case, calculated as $ \frac{f(x_2) - f(x_1)}{x_2 - x_1} $.
- Between each consecutive points:
  - From (0, 2) to (1, 4): $ \frac{4 - 2}{1 - 0} = 2 $
  - From (1, 4) to (2, 6): $ \frac{6 - 4}{2 - 1} = 2 $
  - From (2, 6) to (3, 8): $ \frac{8 - 6}{3 - 2} = 2 $
  - From (3, 8) to (4, 10): $ \frac{10 - 8}{4 - 3} = 2 $
- The slope is the same (2) between all points. Therefore, this statement is False, as there is no point where the slope is steeper than others.
Does the graph have the largest y-intercept?
- The y-intercept appears at $ x = 0 $, where $ f(0) = 2 $. Given the provided table, this is the only y-intercept, so it cannot be said to be the "largest" since it is the only one. Therefore, this statement is True.
Does the graph show a decreasing relationship?
- The graph shows an increasing relationship, as the function values increase (from 2 to 10) as $ x $ increases. Therefore, this statement is False.
Does it have a solution: after 3 blocks of time, you have $8?
- From the table, for $ x = 3 $, $ f(3) = 8 $. Thus, there is indeed a point on the graph that corresponds to having $8 after 3 blocks of time. Therefore, this statement is True.

Summary of True Statements

The graph does not have the steepest slope, as the slope is constant.
The graph has the largest y-intercept (it is the only y-intercept).
The graph does not show a decreasing relationship.
The graph does have a solution; after 3 blocks of time, you have $8.

Final True Statements

The two true statements are:

The graph has the largest y-intercept (2).
It has a solution: after 3 blocks of time, you have $8.

If you need more details or further analysis, feel free to ask!

BTS ARMY · Answer

does the graph have the steepest slope, has the largest y-intercept, shows a decreasing relationship, or has a solution: after 3 blocks of time, you have 8$ x 2 4 6 8 y 13 19 25 31

GPT-4o mini · Answer

Let’s analyze the provided data points and evaluate the statements based on the graph they represent. The data points you provided are as follows:

\[ \begin{array}{|c|c|} \hline x & y \ \hline 2 & 13 \ 4 & 19 \ 6 & 25 \ 8 & 31 \ \hline \end{array} \]

Evaluating Each Statement

Does the graph have the steepest slope?
- To calculate the slope between the points:
  - From (2, 13) to (4, 19): \[ \text{slope} = \frac{19 - 13}{4 - 2} = \frac{6}{2} = 3 \]
  - From (4, 19) to (6, 25): \[ \text{slope} = \frac{25 - 19}{6 - 4} = \frac{6}{2} = 3 \]
  - From (6, 25) to (8, 31): \[ \text{slope} = \frac{31 - 25}{8 - 6} = \frac{6}{2} = 3 \]
- Since all intervals have the same slope of 3, there is no "steepest" slope in this data set. Therefore, this statement is False.
Does the graph have the largest y-intercept?
- From the information provided, we can infer that there is no direct y-intercept given in these points. To find the y-intercept, we would need to extrapolate it from the linear relationship defined by these points. However, the graph does not have a point at $ x = 0 $ to confirm a y-intercept. Therefore, this statement is False since we do not have a defined y-intercept in the provided data.
Does the graph show a decreasing relationship?
- The values of $ y $ are increasing as $ x $ increases (from $ 13 $ to $ 31 $). Thus, the graph displays an increasing relationship, not a decreasing one. Therefore, this statement is False.
Does it have a solution: after 3 blocks of time, you have 8?
- The data provided does not appear to show a value of $ y = 8 $ for $ x = 3 $. In fact, between $ x = 2 $ and $ x = 4 $, the y-values are $ 13 $ and $ 19 $ respectively, indicating that at $ x = 3 $, the corresponding $ y $ value falls between $ 13 $ and $ 19 $. Therefore, this statement is False as well.

Summary of Evaluations

1. The graph does not have the steepest slope (all slopes are equal).
1. The graph does not have the largest y-intercept (no y-intercept provided).
1. The graph does not show a decreasing relationship (it is increasing).
1. The graph does not have a solution for $ y = 8 $ at $ x = 3 $.

Final Conclusion

All of the statements are False based on the given data points. If you have more specific conditions or a different context in which these points should be analyzed, please provide that information!

BTS ARMY · Answer

y = 3x + 7

GPT-4o mini · Answer

The equation $y = 3x + 7$ represents a linear function. Here’s a breakdown of its characteristics: ### 1. Slope and Y-Intercept - **Slope**: The slope of the line is $3$. This indicates that for each increase of $1$ in $x$, $y$ increases by $3$. The slope determines the steepness and direction of the line. - **Y-Intercept**: The y-intercept is $7$. This is the value of $y$ when $x = 0$. So, the point (0, 7) is where the line crosses the y-axis. ### 2. Graphing the Equation To graph the equation, you can plot the y-intercept and use the slope to find another point: - Start at (0, 7) on the y-axis. - From (0, 7), using the slope of $3$ (which can be expressed as $ \frac{3}{1} $), move up $3$ units and right $1$ unit to find another point: - From (0, 7) to (1, 10) (since $7 + 3 = 10$). - You can also move in the opposite direction: from (0, 7) down $3$ units and left $1$ unit to find the point (-1, 4). ### 3. Examples - If you plug in different values of $x$ into the equation, you can find the corresponding $y$ values: - For $x = 0$, $y = 3(0) + 7 = 7$. - For $x = 1$, $y = 3(1) + 7 = 10$. - For $x = -1$, $y = 3(-1) + 7 = 4$. - For $x = 2$, $y = 3(2) + 7 = 13$. ### 4. Implications and Context - The equation can represent a variety of real-world scenarios, such as a relationship between cost and quantity, distance versus time, etc., where $y$ is dependent on $x$. If you have a specific context or question regarding this equation or if you would like me to perform specific calculations or solve a problem related to it, please let me know!