Question
Find the slope and Y intercept that has infinite solutions to the equation
Negative 6X plus 2Y equals 42
The slope would be________.
The Y intercept would be________.
Negative 6X plus 2Y equals 42
The slope would be________.
The Y intercept would be________.
Answers
Answer
Find the slope and white intercept that has infinite solutions to the equation
8X plus 2Y equals 20
The slope would be_______
The Y intercept would be_______
8X plus 2Y equals 20
The slope would be_______
The Y intercept would be_______
Answer
Fill in the blanks at the following system of linear equations as infinite solutions
Why equals negative 7X +9
Y =______x+_______
Why equals negative 7X +9
Y =______x+_______
Answer
Fill the blank so that the following system of linear equations has infinite solutions
Y =-1 X +9
Y=______x+______
Y =-1 X +9
Y=______x+______
Answered by
GPT-4o mini
To determine the slope and the y-intercept of the equation \( -6X + 2Y = 42 \), we first need to rewrite it in slope-intercept form, which is \( Y = mX + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the given equation:
\[
-6X + 2Y = 42
\]
We want to isolate \( Y \). First, add \( 6X \) to both sides:
\[
2Y = 6X + 42
\]
Next, divide every term by \( 2 \):
\[
Y = 3X + 21
\]
Now, we can clearly see that the slope \( m \) is \( 3 \) and the y-intercept \( b \) is \( 21 \).
So the answers are:
The slope would be **3**.
The y-intercept would be **21**.
As for the condition of having infinite solutions, this equation can represent the same line in multiple forms. The equation will have infinite solutions if it is in its original form or in another form equivalent to it.
Starting with the given equation:
\[
-6X + 2Y = 42
\]
We want to isolate \( Y \). First, add \( 6X \) to both sides:
\[
2Y = 6X + 42
\]
Next, divide every term by \( 2 \):
\[
Y = 3X + 21
\]
Now, we can clearly see that the slope \( m \) is \( 3 \) and the y-intercept \( b \) is \( 21 \).
So the answers are:
The slope would be **3**.
The y-intercept would be **21**.
As for the condition of having infinite solutions, this equation can represent the same line in multiple forms. The equation will have infinite solutions if it is in its original form or in another form equivalent to it.
Answered by
GPT-4o mini
To find the slope and y-intercept of the equation \( 8X + 2Y = 20 \), we need to convert it to slope-intercept form \( Y = mX + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the given equation:
\[
8X + 2Y = 20
\]
1. **Isolate \( Y \)** by subtracting \( 8X \) from both sides:
\[
2Y = -8X + 20
\]
2. **Divide every term by 2** to solve for \( Y \):
\[
Y = -4X + 10
\]
Now we can identify the slope and y-intercept:
- The slope \( m \) is **-4**.
- The y-intercept \( b \) is **10**.
Thus, the answers are:
The slope would be **-4**.
The y-intercept would be **10**.
Again, it's important to note that this linear equation will represent a line in a graph, and it will have infinite solutions since any point on that line satisfies the equation.
Starting with the given equation:
\[
8X + 2Y = 20
\]
1. **Isolate \( Y \)** by subtracting \( 8X \) from both sides:
\[
2Y = -8X + 20
\]
2. **Divide every term by 2** to solve for \( Y \):
\[
Y = -4X + 10
\]
Now we can identify the slope and y-intercept:
- The slope \( m \) is **-4**.
- The y-intercept \( b \) is **10**.
Thus, the answers are:
The slope would be **-4**.
The y-intercept would be **10**.
Again, it's important to note that this linear equation will represent a line in a graph, and it will have infinite solutions since any point on that line satisfies the equation.
Answered by
GPT-4o mini
To write a linear equation that would have infinite solutions with the line represented by \( Y = -7X + 9 \), we need to express the second equation in a way that is equivalent to the first equation.
We can multiply the entire equation \( Y = -7X + 9 \) by any non-zero constant. For example, let's multiply by \( 1 \):
\[
Y = 1 \cdot (-7X + 9) \implies Y = -7X + 9
\]
Alternatively, we could multiply by any other non-zero number. For example, if we multiply by \( 2 \):
\[
Y = 2(-7X + 9) \implies Y = -14X + 18
\]
However, to fill in the blanks with a structure similar to the original equation \( Y = -7X + 9 \) while explicitly stating it via a parameter, here's another approach:
Using the same coefficients,
\[
Y = -7X + 9
\]
The blanks would be filled in as follows:
\( Y = -7X + 9 \)
So in your request for the format:
\( Y = \_\_\_\_ X + \_\_\_\_ \)
The answer would be:
\( Y = -7X + 9 \)
To summarize:
- The first blank would be **-7**.
- The second blank would be **9**.
So the final statement is:
\( Y = -7X + 9 \).
We can multiply the entire equation \( Y = -7X + 9 \) by any non-zero constant. For example, let's multiply by \( 1 \):
\[
Y = 1 \cdot (-7X + 9) \implies Y = -7X + 9
\]
Alternatively, we could multiply by any other non-zero number. For example, if we multiply by \( 2 \):
\[
Y = 2(-7X + 9) \implies Y = -14X + 18
\]
However, to fill in the blanks with a structure similar to the original equation \( Y = -7X + 9 \) while explicitly stating it via a parameter, here's another approach:
Using the same coefficients,
\[
Y = -7X + 9
\]
The blanks would be filled in as follows:
\( Y = -7X + 9 \)
So in your request for the format:
\( Y = \_\_\_\_ X + \_\_\_\_ \)
The answer would be:
\( Y = -7X + 9 \)
To summarize:
- The first blank would be **-7**.
- The second blank would be **9**.
So the final statement is:
\( Y = -7X + 9 \).
Answered by
GPT-4o mini
To create a second equation that has infinite solutions with the equation \( Y = -1X + 9 \), we can express it in a different but equivalent form.
An equivalent form can be achieved by multiplying the entire equation by a non-zero constant, or by rearranging it.
For example:
### Original Equation:
\[
Y = -1X + 9
\]
1. **Multiply by 2**:
\[
Y = 2(-1X + 9) \implies Y = -2X + 18
\]
2. **Alternatively, we can just write it as it is**:
\[
Y = -1X + 9
\]
### Therefore,
You can fill in the blanks as follows:
**Using the original equation:**
\[
Y = -1X + 9
\]
This means you would fill in:
- The first blank: **-1**
- The second blank: **9**
So the complete equation would be:
\[
Y = -1X + 9
\]
**Or using the multiplied form:**
\[
Y = -2X + 18
\]
Where you would fill in:
- First blank: **-2**
- Second blank: **18**
So both forms are valid ways to create a second equation that has infinite solutions with the given equation.
An equivalent form can be achieved by multiplying the entire equation by a non-zero constant, or by rearranging it.
For example:
### Original Equation:
\[
Y = -1X + 9
\]
1. **Multiply by 2**:
\[
Y = 2(-1X + 9) \implies Y = -2X + 18
\]
2. **Alternatively, we can just write it as it is**:
\[
Y = -1X + 9
\]
### Therefore,
You can fill in the blanks as follows:
**Using the original equation:**
\[
Y = -1X + 9
\]
This means you would fill in:
- The first blank: **-1**
- The second blank: **9**
So the complete equation would be:
\[
Y = -1X + 9
\]
**Or using the multiplied form:**
\[
Y = -2X + 18
\]
Where you would fill in:
- First blank: **-2**
- Second blank: **18**
So both forms are valid ways to create a second equation that has infinite solutions with the given equation.
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