The cost, (x) for a taxi is given by c (x) = 2x + 4.00, where x is the number of minutes. What does the slope mean for this situation?
The taxi ride costs a total of $4.00.
The rate of change of the cost of the taxi ride is $4.00 per minute.
The rate of change of the cost of the taxi ride is $2.00 per minute.
The taxi ride costs $2.00 per trip.
The correct answer is: The rate of change of the cost of the taxi ride is $2.00 per minute.
The slope in this situation represents the rate of change of the cost of the taxi ride per minute. Since the formula for the cost is c(x) = 2x + 4.00, the coefficient of x (2) represents the rate of change. This means that for each additional minute, the cost of the taxi ride increases by $2.00.
Do you know how to find the slope of a graph?
Yes, the slope of a graph can be found by calculating the change in y-coordinates divided by the change in x-coordinates between two points on the graph.
More formally, the slope of a line can be calculated using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
This is also known as rise over run.
Another way to find the slope of a linear equation in the form y = mx + b, where m is the slope, is to take the coefficient of x. The coefficient of x represents the rate of change of y with respect to x.
Do you know how to find the slope of a graph when one number is negative?
Yes, when calculating the slope of a graph with one of the numbers being negative, you would still use the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
If one of the y-coordinates is negative, it simply means that the line on the graph is decreasing instead of increasing. The slope will also be negative in this case.
For example, if you have two points (x1, y1) and (x2, y2) and the y-coordinates are -4 and 2 respectively, the change in y-coordinates would be:
change in y-coordinates = 2 - (-4) = 2 + 4 = 6
And if the x-coordinates are 3 and 5, the change in x-coordinates would be:
change in x-coordinates = 5 - 3 = 2
Therefore, the slope would be:
slope = 6 / 2 = 3
In this case, the slope would be positive, indicating that the line is increasing as x increases.
Put it in a way a 5th grader understands please, thanks. I'm not in 5th grade I just need u do explain it simpler plz.
Of course! Imagine you have a line on a graph that goes from a point with a y-value of -2, down to a point with a y-value of -6.
To find the slope, you look at how much the y-values change. In this case, the y-value changed from -2 to -6.
So, the change in y-coordinates is -2 (start) - (-6) (end), which can be written as -2 + 6 = 4.
Next, you look at how much the x-values change. If the x-values are going from 3 to 5, the change in x-coordinates is 5 - 3 = 2.
Then, you just divide the change in y-coordinates by the change in x-coordinates to find the slope: 4 / 2 = 2.
So, in this case, the slope is 2. The negative sign in front of the 2 would indicate that the line is going downwards on the graph as you move from left to right.
I hope that explanation was helpful in simpler terms!
So if u go up 2, run 4 thatll get you to 6? Is that hw you got it?
Yes, that's correct! Another way to think about it is using "rise" and "run" to understand slope.
In this case, the slope is 2. This means that for every 4 units you move to the right (run), you go up 2 units (rise) on the graph.
So, if you start at the point (-2, 3) and move 4 units to the right, you would end up at the point (2, 5) since you went up 2 units at a rate of 2/4 (slope).
I hope this explanation clarifies things further for you!
I'm confused still, lol. I want to know how to find the slope of a negative line. Can you write it REALLY simple like this simplest you can? Bc my brain isn't what it used to be.
Sure, I'll break it down as simply as possible for you:
1. Pick two points on the graph that are on the line.
2. Look at how much the y-values change between the two points (this is the rise).
3. Look at how much the x-values change between the two points (this is the run).
4. Divide the rise by the run to find the slope.
5. If the slope is negative, it means the line goes down as you move from left to right on the graph.
I hope this helps simplify it for you! Let me know if you need further clarification. Thank you for your patience!
Ok I think I get it now. So u do rise over run than divide it?
I'm glad to hear that you're starting to understand! That's correct, you first calculate the "rise" (change in y-coordinates) and the "run" (change in x-coordinates), then divide the rise by the run to find the slope of the line.
So, you've got it right: rise over run, and then divide.
If you have any more questions or need further clarification, feel free to ask! I'm here to help.
Can u show me how u divide it? give an example of how to find the slope of a negative line and show all steps plz, really simple tho. thankss
Of course! Let's say we have two points on the graph, (2, -3) and (4, -7), and we want to find the slope of a line passing through these points.
Step 1: Calculate the rise and the run.
- Rise (change in y-coordinates): -7 (y2) - (-3) (y1) = -7 + 3 = -4.
- Run (change in x-coordinates): 4 (x2) - 2 (x1) = 4 - 2 = 2.
Step 2: Divide the rise by the run to find the slope.
- Slope = Rise / Run = -4 / 2 = -2.
Therefore, the slope of the line passing through the points (2, -3) and (4, -7) is -2. This means that for every 2 units you move to the right, the line goes down by 4 units.
I hope this example and explanation help clarify how to find the slope of a negative line. Let me know if you have any more questions.
I didn't get the first one.. :(
No problem! Let's try again with a simpler example:
Example:
Point A is at (1, 5) and Point B is at (3, 3).
Step 1: Calculate the rise and the run.
- Rise (change in y-coordinates): 3 (y2) - 5 (y1) = 3 - 5 = -2. (Since the y-values are decreasing, it is a negative value)
- Run (change in x-coordinates): 3 (x2) - 1 (x1) = 3 - 1 = 2.
Step 2: Divide the rise by the run to find the slope.
- Slope = Rise / Run = -2 / 2 = -1.
Therefore, the slope of the line passing through the points (1, 5) and (3, 3) is -1.
I hope this example makes it simpler for you to understand. Let me know if you have any more questions or need further clarification.
ao if it's negative, u go down?
Yes, if the slope of the line is negative, it means that as you move from left to right along the line on the graph, you are moving downward. This is because the rise (change in y-coordinates) is negative, indicating a decrease in y-values as you move along the line.
So, for a negative slope, the line will go down as you move from left to right.
I hope this clarifies it for you! Let me know if you have any more questions.
Do u know how to determine of the slope of a graph if it's positive, negative, undefined or 0? Plz explain all, but simple, in a way a 5h tgrader can understand.
Of course! Here's a simple way to determine the slope of a graph:
1. Positive slope: If the line goes up as you move from left to right, the slope is positive. This means that y-values increase as x-values increase.
2. Negative slope: If the line goes down as you move from left to right, the slope is negative. This means that y-values decrease as x-values increase.
3. Undefined slope: If the line is vertical (straight up and down), the slope is undefined. This happens when the change in x-coordinates is 0. In this case, the line is not a function.
4. Zero slope: If the line is horizontal (straight left to right), the slope is 0. This happens when the change in y-coordinates is 0.
I hope this simplification helps you understand how to determine if a graph has a positive, negative, undefined, or zero slope. Let me know if you need further explanation or have any more questions!
TYSM THIS WAS SO EASIER TO UNDERSTAND OMG-
You're very welcome! I'm glad to hear that the explanation was helpful and easier to understand. If you have any more questions in the future or need further clarification on any topic, feel free to ask. I'm here to help! Have a great day!
Also how does the y value decrease while x value increase? can u give an example plz?
Certainly! Let's consider an example where the y-value decreases as the x-value increases, resulting in a negative slope.
Example:
Point A is at (1, 5) and Point B is at (3, 3).
Step 1: Calculate the rise and the run.
- Rise (change in y-coordinates): 3 (y2) - 5 (y1) = 3 - 5 = -2.
- Run (change in x-coordinates): 3 (x2) - 1 (x1) = 3 - 1 = 2.
Step 2: Divide the rise by the run to find the slope.
- Slope = Rise / Run = -2 / 2 = -1.
In this example, as you move from Point A (1, 5) to Point B (3, 3) on the graph, the y-value decreases by 2 units (from 5 to 3) while the x-value increases by 2 units. This results in a negative slope of -1, indicating a line that goes downward as you move from left to right.
I hope this example illustrates how the y-value can decrease as the x-value increases when calculating slope. Let me know if you have any more questions!
Can u simplify even more, to like a 2nd grade level
Absolutely! Let's keep it super simple:
Imagine you have a ladder outside. When you go up the ladder, you are climbing higher (positive slope). When you go down the ladder, you are coming down (negative slope).
So, if you have a line that goes up as you move to the right, that's like going up the ladder. It has a positive slope. And if the line goes down as you move to the right, it's like coming down the ladder. That's a negative slope.
I hope this very simple explanation helps! Let me know if you have any more questions or if you need further clarification.
Did u just explain how t ofind a negative slope
I apologize for the oversight. Here's a simpler explanation for understanding a negative slope:
If you're going for a walk in a hilly area, when you walk down a hill, you are going in a negative direction (negative slope). When you walk up a hill, you are going in a positive direction (positive slope).
So, if a line on a graph is going down as you move from left to right, like walking down a hill, it has a negative slope. And if it's going up as you move from left to right, like walking up a hill, it has a positive slope.
I hope this helps clarify how to understand a negative slope. Let me know if you have any more questions!
Explain HOW to find the slope of a negative line? Give examples, but really simple like 4th grade level.
Of course! To find the slope of a negative line, you can follow these steps using simple language:
1. Pick two points on the line.
2. Look at how high or low the points are (rise) and how far apart they are horizontally (run).
3. If the line goes down as you move from left to right, the slope is negative.
4. Calculate how much the line goes down (negative rise) and how far to the side you moved (run).
5. Divide the negative rise by the run to find the slope.
Let's use an example to make it easier:
Example:
Point A is at (1, 6) and Point B is at (3, 2).
Step 1: Calculate the rise and the run.
- Rise (change in y-coordinates): 2 (y2) - 6 (y1) = 2 - 6 = -4.
- Run (change in x-coordinates): 3 (x2) - 1 (x1) = 3 - 1 = 2.
Step 2: Divide the negative rise by the run to find the slope.
- Slope = Rise / Run = -4 / 2 = -2.
So, the slope of the line passing through points (1, 6) and (3, 2) is -2. This means the line goes down by 2 as you move 2 to the right.
I hope this explanation and example at a 4th-grade level help you understand how to find the slope of a negative line. Let me know if you need more help or have any further questions!
What is the slope of the line shown below? (-8 , 5) (0,2)
HELP
To find the slope of a line passing through the points (-8, 5) and (0, 2), we can use the formula for slope:
Slope = (change in y-coordinates) / (change in x-coordinates)
Let's calculate it step by step:
Step 1: Calculate the change in y-coordinates (rise):
- Rise = y2 - y1 = 2 - 5 = -3
Step 2: Calculate the change in x-coordinates (run):
- Run = x2 - x1 = 0 - (-8) = 8
Step 3: Plug the rise and run values into the formula for slope:
Slope = Rise / Run = -3 / 8
Therefore, the slope of the line passing through the points (-8, 5) and (0, 2) is -3/8. This means that for every unit you move to the right (run), the line goes down by 3/8 units (rise).
I hope this helps! Let me know if you need further clarification or have any more questions.
Whats the answer?
The slope of the line passing through the points (-8, 5) and (0, 2) is:
Slope = -3 / 8
This means that for every unit you move to the right along the line, it goes down by 3/8 units.
If you have any more questions or need further assistance, feel free to ask!
tysmm
You're welcome! If you have any more questions in the future, feel free to ask. Have a great day!
Hi again!
Hello! Welcome back! How can I assist you today?
Can we do a spongebob rp?
Of course! I'll play along. Who would you like to be, SpongeBob or another character?
I'll be spongebob, you be mr krabs.
(Ahem, in my best Mr. Krabs voice) Ahoy, SpongeBob! What can I do for ye today, lad?
Hi Mr. Krabs!! How are you doing on this fine day?
Oh, well howdy there, SpongeBob me boy! I'm as happy as a clam at high water seeing you, I am! Just keepin' an eye out for them customers to bring in some more dough for the Krusty Krab. How about you, lad? How's the fry cookin' going today?
I'm doing fabulosss!! Thanks for asking. Though, I have a question. Do you mind if my family comes to eat here?
Oh, me boy, of course not! Bring in the whole family, why don't ya! The more, the merrier at the Krusty Krab. We'll serve up the finest Krabby Patties in all of Bikini Bottom for ya and your family. Just be sure to tell 'em they'll have to pay top dollar for the best darn food in the sea!
That's the problem.. I was also going to ask you if they could eat here... for free...
Oh, SpongeBob me boy, you know I love ye like a son, but free food at the Krusty Krab? That's just not good business, ya see! How about I give you a special employee discount, but the rest of the family will need to pay the regular price. What do you think, lad?
I don't know about that, Mr krabs. I know you are cheap and like money, but it'll be the first time in many years they come to visit me, I haven't seen them in forever and I want a good first impression. I'll make it up to you though. I can clean the whole krusty krab and pay you $500. Please? Only for this special occassion.
(Swipes a tear from the corner of his eye) Oh, SpongeBob me boy, family reunions are important things indeed. All right, I'll make an exception this one time. But you better clean like you've never cleaned before! And the $500 will cover the cost of the food for your family. I'll be expecting that spotless clean, lad!
Hoorayyy!! Oh thank you Mr. Krabs!! I'm gonna head home and get ready for this evening. See ya krabby!
Take care, SpongeBob! I'll see you bright and early tomorrow for work! Enjoy your time with your family. Bye, me boy!
*Later this evening*
(you keep roleplaying as mr.krabs, I'll be spongebob and his family)
Hi Mr. Krabss!! My family will be here shortly. Do you mind if you could try to make this place look.. fancy?!