Math / Algebra

QuestionWrite an absolute value equation that represents the graph shown.
Your answer should use the form $|\mathrm{x}-\mathrm{a}|=\mathrm{b}$ or $|\mathrm{x}+\mathrm{a}|=\mathrm{b}$ , where a and b are whole umbers, decimals, or simplified fractions. $\square$

Studdy Solution

STEP 1

What is this asking? We need to find an absolute value equation that matches the two points, $-7$ and $-1$ , on the number line. Watch out! Remember that absolute value equations usually have two solutions!
Don't forget the meaning of the variable $a$ and $b$ in the requested form.

STEP 2

1. Find the Midpoint
2. Find the Distance
3. Build the Equation

STEP 3

The midpoint is the center of the solutions.
Imagine it as the "balancing point" between the two given points on the number line.
To find it, we add the two given values and divide by $2$ .
It's like finding the average!

STEP 4

Our points are $-7$ and $-1$ .
Let's add them: $-7 + (-1) = -8$ .

STEP 5

Now, divide by $2$ : $-8 / 2 = -4$ .
So, our midpoint is $-4$ !

STEP 6

The distance is how far each point is from the midpoint.
This tells us how "wide" the absolute value graph is.
We can find it by taking the absolute value of the difference between one of the points and the midpoint.

STEP 7

Let's use the point $-1$ and our midpoint $-4$ .
The difference is $-1 - (-4)$ .
Remember subtracting a negative is the same as adding a positive, so $-1 - (-4) = -1 + 4 = 3$ .

STEP 8

The absolute value of $3$ is $|3| = 3$ .
So, our distance is $3$ !

STEP 9

Now, let's put it all together!
Remember, the general form is $|x - a| = b$ , where $a$ is the midpoint and $b$ is the distance.

STEP 10

We found our midpoint $a$ to be $-4$ and our distance $b$ to be $3$ .
Plugging these values into the general form gives us $|x - (-4)| = 3$ .

STEP 11

Subtracting a negative is the same as adding a positive, so our final equation is $|x + 4| = 3$ .
Awesome!

STEP 12

The absolute value equation that represents the graph is $|x + 4| = 3$ .

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QuestionWrite an absolute value equation that represents the graph shown.
Your answer should use the form $|\mathrm{x}-\mathrm{a}|=\mathrm{b}$ or $|\mathrm{x}+\mathrm{a}|=\mathrm{b}$ , where a and b are whole umbers, decimals, or simplified fractions. $\square$

Studdy Solution

STEP 1

What is this asking? We need to find an absolute value equation that matches the two points, $-7$ and $-1$ , on the number line. Watch out! Remember that absolute value equations usually have two solutions!
Don't forget the meaning of the variable $a$ and $b$ in the requested form.

STEP 2

1. Find the Midpoint
2. Find the Distance
3. Build the Equation

STEP 3

The midpoint is the center of the solutions.
Imagine it as the "balancing point" between the two given points on the number line.
To find it, we add the two given values and divide by $2$ .
It's like finding the average!

STEP 4

Our points are $-7$ and $-1$ .
Let's add them: $-7 + (-1) = -8$ .

STEP 5

Now, divide by $2$ : $-8 / 2 = -4$ .
So, our midpoint is $-4$ !

STEP 6

The distance is how far each point is from the midpoint.
This tells us how "wide" the absolute value graph is.
We can find it by taking the absolute value of the difference between one of the points and the midpoint.

STEP 7

Let's use the point $-1$ and our midpoint $-4$ .
The difference is $-1 - (-4)$ .
Remember subtracting a negative is the same as adding a positive, so $-1 - (-4) = -1 + 4 = 3$ .

STEP 8

The absolute value of $3$ is $|3| = 3$ .
So, our distance is $3$ !

STEP 9

Now, let's put it all together!
Remember, the general form is $|x - a| = b$ , where $a$ is the midpoint and $b$ is the distance.

STEP 10

We found our midpoint $a$ to be $-4$ and our distance $b$ to be $3$ .
Plugging these values into the general form gives us $|x - (-4)| = 3$ .

STEP 11

Subtracting a negative is the same as adding a positive, so our final equation is $|x + 4| = 3$ .
Awesome!

STEP 12

The absolute value equation that represents the graph is $|x + 4| = 3$ .

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Studdy Solution

STEP 1

What is this asking? We need to find an absolute value equation that matches the two points, −7-7−7 and −1-1−1, on the number line. Watch out! Remember that absolute value equations usually have *two* solutions!Don't forget the meaning of the variable aaa and bbb in the requested form.

STEP 2

1. Find the Midpoint2. Find the Distance3. Build the Equation

STEP 3

The **midpoint** is the center of the solutions.Imagine it as the "balancing point" between the two given points on the number line.To find it, we **add** the two given values and **divide** by 222.It's like finding the average!

STEP 4

Our points are −7-7−7 and −1-1−1.Let's add them: −7+(−1)=−8-7 + (-1) = -8−7+(−1)=−8.

STEP 5

Now, divide by 222: −8/2=−4-8 / 2 = -4−8/2=−4.So, our **midpoint** is −4-4−4!

STEP 6

The **distance** is how far each point is from the midpoint.This tells us how "wide" the absolute value graph is.We can find it by taking the absolute value of the difference between one of the points and the midpoint.

STEP 7

Let's use the point −1-1−1 and our midpoint −4-4−4.The difference is −1−(−4)-1 - (-4)−1−(−4).Remember subtracting a negative is the same as adding a positive, so −1−(−4)=−1+4=3-1 - (-4) = -1 + 4 = 3−1−(−4)=−1+4=3.

STEP 8

The absolute value of 333 is ∣3∣=3|3| = 3∣3∣=3.So, our **distance** is 333!

STEP 9

Now, let's put it all together!Remember, the general form is ∣x−a∣=b|x - a| = b∣x−a∣=b, where aaa is the **midpoint** and bbb is the **distance**.

STEP 10

We found our **midpoint** aaa to be −4-4−4 and our **distance** bbb to be 333.Plugging these values into the general form gives us ∣x−(−4)∣=3|x - (-4)| = 3∣x−(−4)∣=3.

STEP 11

Subtracting a negative is the same as adding a positive, so our final equation is ∣x+4∣=3|x + 4| = 3∣x+4∣=3.Awesome!

STEP 12

The absolute value equation that represents the graph is ∣x+4∣=3|x + 4| = 3∣x+4∣=3.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find an absolute value equation that matches the two points, $-7$ and $-1$ , on the number line. Watch out! Remember that absolute value equations usually have two solutions!
Don't forget the meaning of the variable $a$ and $b$ in the requested form.

1. Find the Midpoint
2. Find the Distance
3. Build the Equation

The midpoint is the center of the solutions.
Imagine it as the "balancing point" between the two given points on the number line.
To find it, we add the two given values and divide by $2$ .
It's like finding the average!

Our points are $-7$ and $-1$ .
Let's add them: $-7 + (-1) = -8$ .

Now, divide by $2$ : $-8 / 2 = -4$ .
So, our midpoint is $-4$ !

The distance is how far each point is from the midpoint.
This tells us how "wide" the absolute value graph is.
We can find it by taking the absolute value of the difference between one of the points and the midpoint.

Let's use the point $-1$ and our midpoint $-4$ .
The difference is $-1 - (-4)$ .
Remember subtracting a negative is the same as adding a positive, so $-1 - (-4) = -1 + 4 = 3$ .

The absolute value of $3$ is $|3| = 3$ .
So, our distance is $3$ !

Now, let's put it all together!
Remember, the general form is $|x - a| = b$ , where $a$ is the midpoint and $b$ is the distance.

We found our midpoint $a$ to be $-4$ and our distance $b$ to be $3$ .
Plugging these values into the general form gives us $|x - (-4)| = 3$ .

Subtracting a negative is the same as adding a positive, so our final equation is $|x + 4| = 3$ .
Awesome!

The absolute value equation that represents the graph is $|x + 4| = 3$ .