Over which interval does h have a negative average rate of change? Can I ask for a some help please? because I looked at the problems above but it still seems a little confusing to me.

Remember that the rate of change is just the slope of the function. Look back at some of those problems to identify intervals with positive and negative slopes. Hope this helps. <|:)

I need help to solve this and I don't know how to solve this. Here is the question and the problem: Solve the system of equations. −9y+4x−20=0 -7y+16x-80=0

First, it will simplify things if we convert everything to standard form (Ax+By=C) such that the terms without a variable are on the other side of the equation. In this way, we get: 4x-9y=20 and 16x-7y=80 Then, we look for a way to get one of the variables to cancel out with the other equation. Thus, we multiply the entirety of the first equation by 4: 16x-36y=80 and 16x-7y=80 Since we have identical coefficients for the x-variable in both equations, we can subtract one equation from the other so that the x-terms cancel out. 16x-36y=80 -16x-7y =80 ----------------- -43y=0 We have successfully isolated y. From here, we can divide both sides of the equation by -43 to get the value of y: y=0 From here, we can plug the y-value back into one of the previous equations to determine the x-value: 4x-9y=20 4x-9(0)=20 4x=20 This yields the solution: x=5 In these system of equations problems, your strategy should be as follows: choose one variable and eliminate it, solve for the other variable, and then plug the value of the solved variable into the original equation to solve for the unsolved variable.

What interval should I use if I was given 0<t<10?

That is the interval or inputs so you should find the corresponding OUTPUTS.

Find the rate change between f(3)=10 and f(7)=18

You were given two ordered pairs, but in the function notation. Hint: f(x)=y. Use this to identify the (x, y) ordered pairs. Then, use the slope formula to calculate the rate of change. Hope this helps.

_can there be no solution to this type of problem?_

Finding an average rate of change is just finding the slope between 2 points. You can always find the slope. m = (y2-y1)/(x2-x1) The slope could be 0. It could be a number/0 = undefined. Or, it could be an integer or fraction.

Why are we doing the rate of change with these equations instead of how we were taught in the videos?

The formula in these equations is more applicable to the work you will be doing in maths, especially when functions get involved. It still means the same thing, with 'f(b) - f(a)/ b - a' being a different way of writing 'the change in y/ the change in x'. Why the formula is not written in the videos is unclear; I assume it's because writing the same formula over and over again will make the videos feel drawn out.

Main content

Algebra 1

Course: Algebra 1 > Unit 8

Lesson 12: Average rate of change word problems

Average rate of change review

Q: I need help to solve this and I don't know how to solve this. Here is the question and the problem: Solve the system of equations. −9y+4x−20=0 -7y+16x-80=0

First, it will simplify things if we convert everything to standard form (Ax+By=C) such that the terms without a variable are on the other side of the equation. In this way, we get: 4x-9y=20 and 16x-7y=80 Then, we look for a way to get one of the variables to cancel out with the other equation. Thus, we multiply the entirety of the first equation by 4: 16x-36y=80 and 16x-7y=80 Since we have identical coefficients for the x-variable in both equations, we can subtract one equation from the other so that the x-terms cancel out. 16x-36y=80 -16x-7y =80 ----------------- -43y=0 We have successfully isolated y. From here, we can divide both sides of the equation by -43 to get the value of y: y=0 From here, we can plug the y-value back into one of the previous equations to determine the x-value: 4x-9y=20 4x-9(0)=20 4x=20 This yields the solution: x=5 In these system of equations problems, your strategy should be as follows: choose one variable and eliminate it, solve for the other variable, and then plug the value of the solved variable into the original equation to solve for the unsolved variable.

Q: What interval should I use if I was given 0<t<10?

That is the interval or inputs so you should find the corresponding OUTPUTS.

Q: Find the rate change between f(3)=10 and f(7)=18

You were given two ordered pairs, but in the function notation. Hint: f(x)=y. Use this to identify the (x, y) ordered pairs. Then, use the slope formula to calculate the rate of change. Hope this helps.

Q: _can there be no solution to this type of problem?_

Finding an average rate of change is just finding the slope between 2 points. You can always find the slope. m = (y2-y1)/(x2-x1) The slope could be 0. It could be a number/0 = undefined. Or, it could be an integer or fraction.

Q: Why are we doing the rate of change with these equations instead of how we were taught in the videos?

The formula in these equations is more applicable to the work you will be doing in maths, especially when functions get involved. It still means the same thing, with 'f(b) - f(a)/ b - a' being a different way of writing 'the change in y/ the change in x'. Why the formula is not written in the videos is unclear; I assume it's because writing the same formula over and over again will make the videos feel drawn out.

Google Classroom

Review average rate of change and how to apply it to solve problems.

What is average rate of change?

The average rate of change of function f over the interval a, is less than or equal to, x, is less than or equal to, b is given by this expression:

start fraction, f, left parenthesis, b, right parenthesis, minus, f, left parenthesis, a, right parenthesis, divided by, b, minus, a, end fraction

It is a measure of how much the function changed per unit, on average, over that interval.

It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Want to learn more about average rate of change? Check out this video.

Finding average rate of change

Example 1: Average rate of change from graph

Let's find the average rate of change of f over the interval 0, is less than or equal to, x, is less than or equal to, 9:

We can see from the graph that f, left parenthesis, 0, right parenthesis, equals, minus, 7 and f, left parenthesis, 9, right parenthesis, equals, 3.

\begin{aligned} \text{Average rate of change}&=\dfrac{f(9)-f(0)}{9-0} \\\\ &=\dfrac{3-(-7)}{9} \\\\ &=\dfrac{10}{9} \end{aligned}

Example 2: Average rate of change from equation

Let's find the rate of change of g, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x over the interval 1, is less than or equal to, x, is less than or equal to, 6.

g, left parenthesis, 1, right parenthesis, equals, 1, cubed, minus, 9, dot, 1, equals, minus, 8

g, left parenthesis, 6, right parenthesis, equals, 6, cubed, minus, 9, dot, 6, equals, 162

\begin{aligned} \text{Average rate of change}&=\dfrac{g(6)-g(1)}{6-1} \\\\ &=\dfrac{162-(-8)}{5} \\\\ &=34 \end{aligned}

Problem 1

Current

What is the average rate of change of g over the interval minus, 8, is less than or equal to, x, is less than or equal to, minus, 2?

Want to try more problems like this? Check out this exercise.

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Eloy Frias
Posted 4 years ago. Direct link to Eloy Frias's post “Over which interval does ...”
Over which interval does h have a negative average rate of change? Can I ask for a some help please? because I looked at the problems above but it still seems a little confusing to me.
Button navigates to signup pageButton navigates to signup page
(12 votes)
Answer
- jacobson.wpi
  Posted 4 years ago. Direct link to jacobson.wpi's post “Remember that the rate of...”
  Remember that the rate of change is just the slope of the function. Look back at some of those problems to identify intervals with positive and negative slopes.
  
  Hope this helps. <|:)
  Button navigates to signup page
  (20 votes)
s-723724152
Posted 4 years ago. Direct link to s-723724152's post “I need help to solve this...”
I need help to solve this and I don't know how to solve this.

Here is the question and the problem:
Solve the system of equations.
−9y+4x−20=0
-7y+16x-80=0
Button navigates to signup pageComment on s-723724152's post “I need help to solve this...”
(4 votes)
Answer
- Alex T.
  Posted 4 years ago. Direct link to Alex T.'s post “First, it will simplify t...”
  First, it will simplify things if we convert everything to standard form (Ax+By=C) such that the terms without a variable are on the other side of the equation.
  
  In this way, we get:
  
  4x-9y=20 and 16x-7y=80
  
  Then, we look for a way to get one of the variables to cancel out with the other equation. Thus, we multiply the entirety of the first equation by 4:
  
  16x-36y=80 and 16x-7y=80
  
  Since we have identical coefficients for the x-variable in both equations, we can subtract one equation from the other so that the x-terms cancel out.
  
  16x-36y=80
  -16x-7y =80
  -----------------
  -43y=0
  
  We have successfully isolated y. From here, we can divide both sides of the equation by -43 to get the value of y:
  
  y=0
  
  From here, we can plug the y-value back into one of the previous equations to determine the x-value:
  
  4x-9y=20
  4x-9(0)=20
  4x=20
  
  This yields the solution:
  
  x=5
  
  In these system of equations problems, your strategy should be as follows: choose one variable and eliminate it, solve for the other variable, and then plug the value of the solved variable into the original equation to solve for the unsolved variable.
  Comment on Alex T.'s post “First, it will simplify t...”
  (6 votes)
913498
Posted 5 months ago. Direct link to 913498's post “Find the rate change betw...”
Find the rate change between f(3)=10 and f(7)=18
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Kim Seidel
  Posted 5 months ago. Direct link to Kim Seidel's post “You were given two ordere...”
  You were given two ordered pairs, but in the function notation. Hint: f(x)=y. Use this to identify the (x, y) ordered pairs. Then, use the slope formula to calculate the rate of change.
  
  Hope this helps.
  Button navigates to signup page
  (5 votes)
mernellejoy
Posted 3 years ago. Direct link to mernellejoy's post “What interval should I us...”
What interval should I use if I was given 0<t<10?
Button navigates to signup pageComment on mernellejoy's post “What interval should I us...”
(3 votes)
Answer
- Mr. Harlston
  Posted 2 years ago. Direct link to Mr. Harlston's post “That is the interval or i...”
  That is the interval or inputs so you should find the corresponding OUTPUTS.
  Comment on Mr. Harlston's post “That is the interval or i...”
  (3 votes)
corny@hornydog6969
Posted a year ago. Direct link to corny@hornydog6969's post “_can there be no solution...”
can there be no solution to this type of problem?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Kim Seidel
  Posted a year ago. Direct link to Kim Seidel's post “Finding an average rate o...”
  Finding an average rate of change is just finding the slope between 2 points. You can always find the slope.
  m = (y2-y1)/(x2-x1)
  The slope could be 0. It could be a number/0 = undefined. Or, it could be an integer or fraction.
  Button navigates to signup page
  (4 votes)
Lili
Posted 6 months ago. Direct link to Lili's post “Why are we doing the rate...”
Why are we doing the rate of change with these equations instead of how we were taught in the videos?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Logan
  Posted 5 months ago. Direct link to Logan's post “The formula in these equa...”
  The formula in these equations is more applicable to the work you will be doing in maths, especially when functions get involved. It still means the same thing, with 'f(b) - f(a)/ b - a' being a different way of writing 'the change in y/ the change in x'.
  
  Why the formula is not written in the videos is unclear; I assume it's because writing the same formula over and over again will make the videos feel drawn out.
  Button navigates to signup page
  (2 votes)
申良平
Posted 5 years ago. Direct link to 申良平's post “Should the name of "Mean ...”
Should the name of "Mean Value Theorem" asked in the practice questions in this unit be specified as "Mean Value Theorem for for derivatives" to distinguish that for integrals?
Button navigates to signup pageComment on 申良平's post “Should the name of "Mean ...”
(2 votes)
Answer
Teairra Pough
Posted 4 years ago. Direct link to Teairra Pough's post “What is the average rate ...”
What is the average rate of change of F over the interval -7≤x≤2?
Button navigates to signup pageComment on Teairra Pough's post “What is the average rate ...”
(2 votes)
Answer
Michael Pinion
Posted 16 days ago. Direct link to Michael Pinion's post “what if the dots on your ...”
what if the dots on your graft land on the number line itself. Like (-6) and (-4). Would that mean that the other number is "0" for both?
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(2 votes)
Answer
- Thursday
  Posted a day ago. Direct link to Thursday's post “Yes. If the dot lands on ...”
  Yes. If the dot lands on the horizontal line, it is called the x-intercept. While the dot which lands on a vertical line is called the y-intercept. Basically, x-intercept is when x > 0 and y = 0. While y-intercept is when y > 0 and x = 0.
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  (1 vote)
eabney24
Posted 2 months ago. Direct link to eabney24's post “How do you neaten the lin...”
How do you neaten the lines on the graphs? Mine were always wiggly and they made me get multiple questions wrong.
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(2 votes)
Answer