Question
Write an equation from slope-intercept form (
y
=
m
x
+
b
y=mx+b ) from the table below. Click Here for Help Video.
x
x
y
y
0
0
2
2
−
1
−1
−
4
−4
−
2
−2
−
10
−10
−
3
−3
−
16
−16
y
=
y =
x
+
x +
Answers
Answer
wrong
Answer
y=____x+_____ find the answer!
Answer
wrong here's the table to help x
y
y
0
0
2
2
−
1
−1
−
4
−4
−
2
−2
−
10
−10
−
3
−3
−
16
−16
y
y
0
0
2
2
−
1
−1
−
4
−4
−
2
−2
−
10
−10
−
3
−3
−
16
−16
Answer
ITS STILL WRONG USE (
y
=
m
x
+
b
y=mx+b ) FROM THE TABLE
y
=
m
x
+
b
y=mx+b ) FROM THE TABLE
Answered by
GPT-4o mini
To write the equation in slope-intercept form \( y = mx + b \), we first need to find the slope \( m \) and the y-intercept \( b \) from the provided points in the table.
Given points:
- (0, 0)
- (2, 2)
- (-1, -1)
- (-4, -4)
- (-2, -2)
- (-10, -10)
- (-3, -3)
- (-16, -16)
We can observe that all these points lie on a line where each \( x \) value corresponds to the same \( y \) value.
Let's calculate the slope \( m \). The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 0) and (2, 2):
\[
m = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1
\]
Now we need to find the y-intercept \( b \). Since one of the points is (0, 0), we can see that when \( x = 0 \), \( y = 0 \). Thus, the y-intercept \( b = 0 \).
Now we can write the equation:
\[
y = 1x + 0 \quad \text{or simply} \quad y = x
\]
Therefore, the final equation in slope-intercept form is:
\[
y = x
\]
Given points:
- (0, 0)
- (2, 2)
- (-1, -1)
- (-4, -4)
- (-2, -2)
- (-10, -10)
- (-3, -3)
- (-16, -16)
We can observe that all these points lie on a line where each \( x \) value corresponds to the same \( y \) value.
Let's calculate the slope \( m \). The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 0) and (2, 2):
\[
m = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1
\]
Now we need to find the y-intercept \( b \). Since one of the points is (0, 0), we can see that when \( x = 0 \), \( y = 0 \). Thus, the y-intercept \( b = 0 \).
Now we can write the equation:
\[
y = 1x + 0 \quad \text{or simply} \quad y = x
\]
Therefore, the final equation in slope-intercept form is:
\[
y = x
\]
Answered by
GPT-4o mini
I apologize for the confusion! Let's analyze the data again, step-by-step.
Given the points from the table:
- (0, 0)
- (2, 2)
- (-1, -1)
- (-4, -4)
- (-2, -2)
- (-10, -10)
- (-3, -3)
- (-16, -16)
All these points are aligned along the line \(y = x\), which means:
1. **Finding the Slope (m)**:
The rise over run formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can take any two points — for example, (0, 0) and (2, 2):
\[
m = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1
\]
2. **Y-Intercept (b)**:
The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the point (0, 0), we see that \( b = 0 \).
Putting it all together gives us the equation in slope-intercept form:
\[
y = 1x + 0
\]
or simply:
\[
y = x
\]
However, if the intent was to find a different equation based on the specific input or if you needed a different interpretation, please provide clarification or guidance, so I can assist you accurately. Thank you!
Given the points from the table:
- (0, 0)
- (2, 2)
- (-1, -1)
- (-4, -4)
- (-2, -2)
- (-10, -10)
- (-3, -3)
- (-16, -16)
All these points are aligned along the line \(y = x\), which means:
1. **Finding the Slope (m)**:
The rise over run formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can take any two points — for example, (0, 0) and (2, 2):
\[
m = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1
\]
2. **Y-Intercept (b)**:
The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the point (0, 0), we see that \( b = 0 \).
Putting it all together gives us the equation in slope-intercept form:
\[
y = 1x + 0
\]
or simply:
\[
y = x
\]
However, if the intent was to find a different equation based on the specific input or if you needed a different interpretation, please provide clarification or guidance, so I can assist you accurately. Thank you!
Answered by
GPT-4o mini
I apologize for any earlier confusion. Let's correctly express the relationship from the given table in the form \(y = mx + b\).
### Given points:
- (0, 0)
- (2, 2)
- (-1, -1)
- (-4, -4)
- (-2, -2)
- (-10, -10)
- (-3, -3)
- (-16, -16)
### The Analysis:
**1. Finding the Slope (m):**
Using two points, for example, (0, 0) and (2, 2):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1
\]
**2. Finding the Y-Intercept (b):**
The y-intercept can be found from the point (0, 0):
When \( x = 0 \), \( y = 0 \), so:
\[
b = 0
\]
### Putting it All Together:
The slope-intercept form of the equation is:
\[
y = mx + b
\]
Substituting \( m \) and \( b \) into the equation gives us:
\[
y = 1x + 0
\]
or simply:
\[
y = x
\]
However, following the format you requested of \( y = \_\_\_x + \_\_\_\):
### Final Form:
- \( m = 1 \)
- \( b = 0 \)
So the equation filled in would be:
\[
y = 1x + 0
\]
Thus, in the format you've asked for:
**y = 1x + 0**.
### Given points:
- (0, 0)
- (2, 2)
- (-1, -1)
- (-4, -4)
- (-2, -2)
- (-10, -10)
- (-3, -3)
- (-16, -16)
### The Analysis:
**1. Finding the Slope (m):**
Using two points, for example, (0, 0) and (2, 2):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1
\]
**2. Finding the Y-Intercept (b):**
The y-intercept can be found from the point (0, 0):
When \( x = 0 \), \( y = 0 \), so:
\[
b = 0
\]
### Putting it All Together:
The slope-intercept form of the equation is:
\[
y = mx + b
\]
Substituting \( m \) and \( b \) into the equation gives us:
\[
y = 1x + 0
\]
or simply:
\[
y = x
\]
However, following the format you requested of \( y = \_\_\_x + \_\_\_\):
### Final Form:
- \( m = 1 \)
- \( b = 0 \)
So the equation filled in would be:
\[
y = 1x + 0
\]
Thus, in the format you've asked for:
**y = 1x + 0**.
Answered by
GPT-4o mini
Thank you for your clarification. Let’s use the points from the table you provided to derive the equation correctly.
### Provided Points:
- (0, 0)
- (2, 2)
- (-1, -1)
- (-4, -4)
- (-2, -2)
- (-10, -10)
- (-3, -3)
- (-16, -16)
### Analyzing the Data
1. **Identify Points**:
You have provided several points. Let's identify valid pairs from the ones that maintain the same linear relationship.
From the pairs, they appear to follow the line equation.
2. **Finding the Slope (m)**:
The slope can still be calculated using any two points. For example, using points (2, 2) and (0, 0):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = 1
\]
So the slope \( m = 1 \).
3. **Finding the Y-Intercept (b)**:
You can find \( b \) by utilizing the point (0, 0):
\[
b = 0
\]
However, considering the negative values correctly, I see they all seem to maintain a linear pattern through the origin.
### Let’s Correctly Formulate the Equation
Given the nature of the points, they suggest a relationship of \( y = mx + b \):
Since the slope is constant at 1, despite toggling through negative points, we should adjust for this under the overall format.
#### Final Equation Format
To express in the correct form \( y = mx + b \):
### Conclusion:
**The correct linear equation based on the pattern and your points provided is:**
\[
y = 1x + 0
\]
However, if we include a broader perspective of negative values derived uniquely from this consistent decrement through all values to encompass negative slopes:
Should you need to identify the consistent pattern through any negative associations based on the negative formula:
- For instance re-evaluating those negatives for potential different relationships or contextual shifts as required for transformations yielding distinctly different intercepts.
Please let me know if you are looking for a specific interpretation or alternative models aligning with the derived behavior of negative effects within plotted points! Thank you for your patience!
### Provided Points:
- (0, 0)
- (2, 2)
- (-1, -1)
- (-4, -4)
- (-2, -2)
- (-10, -10)
- (-3, -3)
- (-16, -16)
### Analyzing the Data
1. **Identify Points**:
You have provided several points. Let's identify valid pairs from the ones that maintain the same linear relationship.
From the pairs, they appear to follow the line equation.
2. **Finding the Slope (m)**:
The slope can still be calculated using any two points. For example, using points (2, 2) and (0, 0):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = 1
\]
So the slope \( m = 1 \).
3. **Finding the Y-Intercept (b)**:
You can find \( b \) by utilizing the point (0, 0):
\[
b = 0
\]
However, considering the negative values correctly, I see they all seem to maintain a linear pattern through the origin.
### Let’s Correctly Formulate the Equation
Given the nature of the points, they suggest a relationship of \( y = mx + b \):
Since the slope is constant at 1, despite toggling through negative points, we should adjust for this under the overall format.
#### Final Equation Format
To express in the correct form \( y = mx + b \):
### Conclusion:
**The correct linear equation based on the pattern and your points provided is:**
\[
y = 1x + 0
\]
However, if we include a broader perspective of negative values derived uniquely from this consistent decrement through all values to encompass negative slopes:
Should you need to identify the consistent pattern through any negative associations based on the negative formula:
- For instance re-evaluating those negatives for potential different relationships or contextual shifts as required for transformations yielding distinctly different intercepts.
Please let me know if you are looking for a specific interpretation or alternative models aligning with the derived behavior of negative effects within plotted points! Thank you for your patience!
Answered by
GPT-4o mini
I apologize for the confusion earlier. Let's extract the relationship strictly from the provided data. Thank you for your patience!
### Given Points from the Table:
\[
\begin{align*}
(0, 0) \\
(2, 2) \\
(-1, -1) \\
(-4, -4) \\
(-2, -2) \\
(-10, -10) \\
(-3, -3) \\
(-16, -16) \\
\end{align*}
\]
### Identifying the Pattern
From the pairs, it seems all points suggest a consistent relationship that can be linear.
### Finding the Slope (m)
We can take any two points. Let's choose (2, 2) and (0, 0):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
= \frac{2 - 0}{2 - 0}
= \frac{2}{2}
= 1
\]
### Finding the Y-Intercept (b)
Since (0, 0) is one of the points, we can see that the y-intercept \( b = 0 \).
### Form the Linear Equation
Using the slope \( m \) and the intercept \( b \), we can write the equation in the form \( y = mx + b \):
Substituting \( m \) and \( b \):
\[
y = 1x + 0
\]
Or simplified:
\[
y = x
\]
However, since it appears you want explicitly in the format \( y = mx + b \):
### Final Result:
Thus, in the explicit format of \( y = mx + b \):
\[
y = 1x + 0
\]
If there's a specific result or further requirement regarding alternative interpretations of multiple slopes or variances within these pairs, please let me know! Thank you for your understanding!
### Given Points from the Table:
\[
\begin{align*}
(0, 0) \\
(2, 2) \\
(-1, -1) \\
(-4, -4) \\
(-2, -2) \\
(-10, -10) \\
(-3, -3) \\
(-16, -16) \\
\end{align*}
\]
### Identifying the Pattern
From the pairs, it seems all points suggest a consistent relationship that can be linear.
### Finding the Slope (m)
We can take any two points. Let's choose (2, 2) and (0, 0):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
= \frac{2 - 0}{2 - 0}
= \frac{2}{2}
= 1
\]
### Finding the Y-Intercept (b)
Since (0, 0) is one of the points, we can see that the y-intercept \( b = 0 \).
### Form the Linear Equation
Using the slope \( m \) and the intercept \( b \), we can write the equation in the form \( y = mx + b \):
Substituting \( m \) and \( b \):
\[
y = 1x + 0
\]
Or simplified:
\[
y = x
\]
However, since it appears you want explicitly in the format \( y = mx + b \):
### Final Result:
Thus, in the explicit format of \( y = mx + b \):
\[
y = 1x + 0
\]
If there's a specific result or further requirement regarding alternative interpretations of multiple slopes or variances within these pairs, please let me know! Thank you for your understanding!
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