Question
What is the y-intercept of the line that goes through the points in the table?
x: -12, -9, -6, -3, 0
y:1, -3, -7, -11, -15
x: -12, -9, -6, -3, 0
y:1, -3, -7, -11, -15
Answers
Answer
What is the slope of the line that goes through the points in the table?
Answer
wronggg
Answer
what is the slope of the line that goes through the points in the table?
M =
M =
Answer
What is the slope of the line that goes through the points in the table?
M=
4
1/4
1/3
1/6
3
6
M=
4
1/4
1/3
1/6
3
6
Answered by
GPT-4o mini
To find the y-intercept of the line that goes through the points given in the table, we can first identify the relationship between the x and y values.
The points from the table are:
- (-12, 1)
- (-9, -3)
- (-6, -7)
- (-3, -11)
- (0, -15)
A common way to find the y-intercept is to find the equation of the line in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
### Step 1: Find the slope (m)
To calculate the slope (\( m \)), we use two points. Let's use the points (-12, 1) and (0, -15):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, choose (-12, 1) as (x1, y1) and (0, -15) as (x2, y2):
\[
m = \frac{-15 - 1}{0 - (-12)} = \frac{-16}{12} = -\frac{4}{3}
\]
### Step 2: Use the slope to find the y-intercept (b)
We can use the slope-intercept form to find \( b \). We'll use the point (0, -15):
\[
y = mx + b
\]
Substituting \( m \) and the coordinates of the point (0, -15):
\[
-15 = -\frac{4}{3}(0) + b
\]
\[
-15 = b
\]
Thus, the y-intercept \( b \) is -15.
### Conclusion
The y-intercept of the line that goes through the points in the table is \(-15\).
The points from the table are:
- (-12, 1)
- (-9, -3)
- (-6, -7)
- (-3, -11)
- (0, -15)
A common way to find the y-intercept is to find the equation of the line in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
### Step 1: Find the slope (m)
To calculate the slope (\( m \)), we use two points. Let's use the points (-12, 1) and (0, -15):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, choose (-12, 1) as (x1, y1) and (0, -15) as (x2, y2):
\[
m = \frac{-15 - 1}{0 - (-12)} = \frac{-16}{12} = -\frac{4}{3}
\]
### Step 2: Use the slope to find the y-intercept (b)
We can use the slope-intercept form to find \( b \). We'll use the point (0, -15):
\[
y = mx + b
\]
Substituting \( m \) and the coordinates of the point (0, -15):
\[
-15 = -\frac{4}{3}(0) + b
\]
\[
-15 = b
\]
Thus, the y-intercept \( b \) is -15.
### Conclusion
The y-intercept of the line that goes through the points in the table is \(-15\).
Answered by
GPT-4o mini
To determine the slope of the line that goes through the points from the table, we can use any two points from the data provided.
The points from the table are:
- \((-12, 1)\)
- \((-9, -3)\)
- \((-6, -7)\)
- \((-3, -11)\)
- \((0, -15)\)
### Formula for Slope
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
### Step 1: Choose two points
Let's calculate the slope using the points \((-12, 1)\) and \((-3, -11)\).
- \((x_1, y_1) = (-12, 1)\)
- \((x_2, y_2) = (-3, -11)\)
### Step 2: Substitute into the slope formula
Now, substituting the values into the slope formula:
\[
m = \frac{-11 - 1}{-3 - (-12)} = \frac{-12}{-3 + 12} = \frac{-12}{9} = -\frac{4}{3}
\]
### Conclusion
Thus, the slope of the line that goes through the points in the table is \(-\frac{4}{3}\).
The points from the table are:
- \((-12, 1)\)
- \((-9, -3)\)
- \((-6, -7)\)
- \((-3, -11)\)
- \((0, -15)\)
### Formula for Slope
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
### Step 1: Choose two points
Let's calculate the slope using the points \((-12, 1)\) and \((-3, -11)\).
- \((x_1, y_1) = (-12, 1)\)
- \((x_2, y_2) = (-3, -11)\)
### Step 2: Substitute into the slope formula
Now, substituting the values into the slope formula:
\[
m = \frac{-11 - 1}{-3 - (-12)} = \frac{-12}{-3 + 12} = \frac{-12}{9} = -\frac{4}{3}
\]
### Conclusion
Thus, the slope of the line that goes through the points in the table is \(-\frac{4}{3}\).
Answered by
GPT-4o mini
I apologize for any confusion in my previous messages! Let’s recalculate the slope using the points again carefully to ensure accuracy.
The points provided are:
- \((-12, 1)\)
- \((-9, -3)\)
- \((-6, -7)\)
- \((-3, -11)\)
- \((0, -15)\)
### Formula for Slope
The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
### Choose Two Points
Let's use the points \((-12, 1)\) and \((-3, -11)\):
- \((x_1, y_1) = (-12, 1)\)
- \((x_2, y_2) = (-3, -11)\)
### Substitute into the Slope Formula
Now substituting the values:
\[
m = \frac{-11 - 1}{-3 - (-12)}
\]
\[
m = \frac{-12}{-3 + 12}
\]
\[
m = \frac{-12}{9} = -\frac{4}{3}
\]
### Verify with Another Pair of Points
Let’s verify by calculating the slope between two different points, like \((-9, -3)\) and \((-6, -7)\):
- \((x_1, y_1) = (-9, -3)\)
- \((x_2, y_2) = (-6, -7)\)
### Substitute into the Slope Formula Again
\[
m = \frac{-7 - (-3)}{-6 - (-9)}
\]
\[
m = \frac{-7 + 3}{-6 + 9}
\]
\[
m = \frac{-4}{3} = -\frac{4}{3}
\]
### Conclusion
The slope of the line that goes through the points in the table is consistently \(-\frac{4}{3}\). If you have any specific points or methods in mind that I should consider, please let me know!
The points provided are:
- \((-12, 1)\)
- \((-9, -3)\)
- \((-6, -7)\)
- \((-3, -11)\)
- \((0, -15)\)
### Formula for Slope
The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
### Choose Two Points
Let's use the points \((-12, 1)\) and \((-3, -11)\):
- \((x_1, y_1) = (-12, 1)\)
- \((x_2, y_2) = (-3, -11)\)
### Substitute into the Slope Formula
Now substituting the values:
\[
m = \frac{-11 - 1}{-3 - (-12)}
\]
\[
m = \frac{-12}{-3 + 12}
\]
\[
m = \frac{-12}{9} = -\frac{4}{3}
\]
### Verify with Another Pair of Points
Let’s verify by calculating the slope between two different points, like \((-9, -3)\) and \((-6, -7)\):
- \((x_1, y_1) = (-9, -3)\)
- \((x_2, y_2) = (-6, -7)\)
### Substitute into the Slope Formula Again
\[
m = \frac{-7 - (-3)}{-6 - (-9)}
\]
\[
m = \frac{-7 + 3}{-6 + 9}
\]
\[
m = \frac{-4}{3} = -\frac{4}{3}
\]
### Conclusion
The slope of the line that goes through the points in the table is consistently \(-\frac{4}{3}\). If you have any specific points or methods in mind that I should consider, please let me know!
Answered by
GPT-4o mini
To determine the slope of the line that goes through the points in the table, we first need to identify whether there is a consistent pattern in the coordinates given. Let’s use the coordinates provided:
- \((-12, 1)\)
- \((-9, -3)\)
- \((-6, -7)\)
- \((-3, -11)\)
- \((0, -15)\)
### Calculation of the Slope (M)
We'll calculate the slope using two points. Let's use \((-12, 1)\) and \((-9, -3)\):
1. Identify the coordinates:
- \((x_1, y_1) = (-12, 1)\)
- \((x_2, y_2) = (-9, -3)\)
2. Use the slope formula:
\[
M = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values:
\[
M = \frac{-3 - 1}{-9 - (-12)}
\]
\[
M = \frac{-4}{-9 + 12}
\]
\[
M = \frac{-4}{3}
\]
Thus, the slope \( M \) for the line that goes through the points is:
\[
M = -\frac{4}{3}
\]
### Conclusion
The slope \( M \) of the line is \(-\frac{4}{3}\). If you have any further questions or need additional calculations, let me know!
- \((-12, 1)\)
- \((-9, -3)\)
- \((-6, -7)\)
- \((-3, -11)\)
- \((0, -15)\)
### Calculation of the Slope (M)
We'll calculate the slope using two points. Let's use \((-12, 1)\) and \((-9, -3)\):
1. Identify the coordinates:
- \((x_1, y_1) = (-12, 1)\)
- \((x_2, y_2) = (-9, -3)\)
2. Use the slope formula:
\[
M = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values:
\[
M = \frac{-3 - 1}{-9 - (-12)}
\]
\[
M = \frac{-4}{-9 + 12}
\]
\[
M = \frac{-4}{3}
\]
Thus, the slope \( M \) for the line that goes through the points is:
\[
M = -\frac{4}{3}
\]
### Conclusion
The slope \( M \) of the line is \(-\frac{4}{3}\). If you have any further questions or need additional calculations, let me know!
Answered by
GPT-4o mini
To determine the slope (\(M\)) of the line that goes through the points in the table you provided, let's summarize the key points. If the earlier calculations using your provided points were correct, you already have points noted:
- \((-12, 1)\)
- \((-9, -3)\)
- \((-6, -7)\)
- \((-3, -11)\)
- \((0, -15)\)
From previous calculations, we found the slope as:
\[
M = \frac{y_2 - y_1}{x_2 - x_1} = -\frac{4}{3}
\]
However, based on the options you've provided:
- \(4\)
- \(\frac{1}{4}\)
- \(\frac{1}{3}\)
- \(\frac{1}{6}\)
- \(3\)
- \(6\)
### Conclusion
The slope from the points calculated does not match any of the provided options. It's clear there might be a misunderstanding or mismatch in the points provided versus the options for slope.
To find which of the options fits best, let's check the slope for example pairs of your given points to see if any provide values in your selection.
### Checking slope between other pairs:
Let's quickly check the slope between two closer points for median approximation.
Using points \((-6, -7)\) and \((-3, -11)\):
\[
M = \frac{-11 - (-7)}{-3 - (-6)} = \frac{-11 + 7}{-3 + 6} = \frac{-4}{3}
\]
Switching to other points or pairs likely does not yield simple integers or fractions connecting to 1, 3, or low fractions on that scale per iterative check on what combinations we have.
### Final Answer
None of the provided multiples you gave match with \( -\frac{4}{3} \), which implies there might be specific missed data directives regarding right pairs linking based on the options you're supplying—these don't yield accurate slope value to match given choices.
If you have revised points or want specific pairs examined that yield one of the stated options, please clarify!
- \((-12, 1)\)
- \((-9, -3)\)
- \((-6, -7)\)
- \((-3, -11)\)
- \((0, -15)\)
From previous calculations, we found the slope as:
\[
M = \frac{y_2 - y_1}{x_2 - x_1} = -\frac{4}{3}
\]
However, based on the options you've provided:
- \(4\)
- \(\frac{1}{4}\)
- \(\frac{1}{3}\)
- \(\frac{1}{6}\)
- \(3\)
- \(6\)
### Conclusion
The slope from the points calculated does not match any of the provided options. It's clear there might be a misunderstanding or mismatch in the points provided versus the options for slope.
To find which of the options fits best, let's check the slope for example pairs of your given points to see if any provide values in your selection.
### Checking slope between other pairs:
Let's quickly check the slope between two closer points for median approximation.
Using points \((-6, -7)\) and \((-3, -11)\):
\[
M = \frac{-11 - (-7)}{-3 - (-6)} = \frac{-11 + 7}{-3 + 6} = \frac{-4}{3}
\]
Switching to other points or pairs likely does not yield simple integers or fractions connecting to 1, 3, or low fractions on that scale per iterative check on what combinations we have.
### Final Answer
None of the provided multiples you gave match with \( -\frac{4}{3} \), which implies there might be specific missed data directives regarding right pairs linking based on the options you're supplying—these don't yield accurate slope value to match given choices.
If you have revised points or want specific pairs examined that yield one of the stated options, please clarify!
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