Question
What is the slope of the line that goes through the points?
x: 0, 10,20
y: 8, 4,0
x: 0, 10,20
y: 8, 4,0
Answers
Answered by
GPT-4o mini
To find the slope of the line that passes through the points given, you can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's use the points \((0, 8)\) and \((20, 0)\) for this calculation:
- \(x_1 = 0\), \(y_1 = 8\)
- \(x_2 = 20\), \(y_2 = 0\)
Substituting the values into the slope formula:
\[
m = \frac{0 - 8}{20 - 0} = \frac{-8}{20} = -\frac{2}{5}
\]
Thus, the slope of the line is \(-\frac{2}{5}\).
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's use the points \((0, 8)\) and \((20, 0)\) for this calculation:
- \(x_1 = 0\), \(y_1 = 8\)
- \(x_2 = 20\), \(y_2 = 0\)
Substituting the values into the slope formula:
\[
m = \frac{0 - 8}{20 - 0} = \frac{-8}{20} = -\frac{2}{5}
\]
Thus, the slope of the line is \(-\frac{2}{5}\).
Answer
wrong aaaaa
Answered by
GPT-4o mini
I apologize for any confusion. Let's re-evaluate the problem step-by-step to ensure we calculate the slope correctly. Given the points:
- Point 1: \( (0, 8) \)
- Point 2: \( (10, 4) \)
- Point 3: \( (20, 0) \)
We need to calculate the slope using any two of these points. I will first calculate the slope between the points \((0, 8)\) and \((10, 4)\) and then between \((10, 4)\) and \((20, 0)\) to ensure accuracy.
### Slope between (0, 8) and (10, 4):
Using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):
- \(x_1 = 0\), \(y_1 = 8\)
- \(x_2 = 10\), \(y_2 = 4\)
Substituting the values:
\[
m = \frac{4 - 8}{10 - 0} = \frac{-4}{10} = -\frac{2}{5}
\]
### Slope between (10, 4) and (20, 0):
Now using the points \((10, 4)\) and \((20, 0)\):
- \(x_1 = 10\), \(y_1 = 4\)
- \(x_2 = 20\), \(y_2 = 0\)
Substituting the values:
\[
m = \frac{0 - 4}{20 - 10} = \frac{-4}{10} = -\frac{2}{5}
\]
### Conclusion
The slope between both pairs of points gives the same result of \(-\frac{2}{5}\). So, it seems the calculation is consistent and accurate.
If you meant to ask for something specific or if there's a different section of the problem you'd like to go over, please let me know, and I'd be happy to assist further!
- Point 1: \( (0, 8) \)
- Point 2: \( (10, 4) \)
- Point 3: \( (20, 0) \)
We need to calculate the slope using any two of these points. I will first calculate the slope between the points \((0, 8)\) and \((10, 4)\) and then between \((10, 4)\) and \((20, 0)\) to ensure accuracy.
### Slope between (0, 8) and (10, 4):
Using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):
- \(x_1 = 0\), \(y_1 = 8\)
- \(x_2 = 10\), \(y_2 = 4\)
Substituting the values:
\[
m = \frac{4 - 8}{10 - 0} = \frac{-4}{10} = -\frac{2}{5}
\]
### Slope between (10, 4) and (20, 0):
Now using the points \((10, 4)\) and \((20, 0)\):
- \(x_1 = 10\), \(y_1 = 4\)
- \(x_2 = 20\), \(y_2 = 0\)
Substituting the values:
\[
m = \frac{0 - 4}{20 - 10} = \frac{-4}{10} = -\frac{2}{5}
\]
### Conclusion
The slope between both pairs of points gives the same result of \(-\frac{2}{5}\). So, it seems the calculation is consistent and accurate.
If you meant to ask for something specific or if there's a different section of the problem you'd like to go over, please let me know, and I'd be happy to assist further!
Answer
What is the y-intercept of the line that goes through the points?
Answered by
GPT-4o mini
To find the \(y\)-intercept of the line that goes through the points, we can use the slope-intercept form of the line equation, which is:
\[
y = mx + b
\]
where \(m\) is the slope, and \(b\) is the y-intercept.
From our previous calculation, we found that the slope \(m\) is \(-\frac{2}{5}\).
We can use one of the points to solve for \(b\). Let's use the point \((0, 8)\):
Using the point \( (x, y) = (0, 8) \):
\[
8 = -\frac{2}{5}(0) + b
\]
This simplifies to:
\[
8 = b
\]
Thus, the \(y\)-intercept \(b\) is \(8\).
### Conclusion
The \(y\)-intercept of the line is \(8\).
\[
y = mx + b
\]
where \(m\) is the slope, and \(b\) is the y-intercept.
From our previous calculation, we found that the slope \(m\) is \(-\frac{2}{5}\).
We can use one of the points to solve for \(b\). Let's use the point \((0, 8)\):
Using the point \( (x, y) = (0, 8) \):
\[
8 = -\frac{2}{5}(0) + b
\]
This simplifies to:
\[
8 = b
\]
Thus, the \(y\)-intercept \(b\) is \(8\).
### Conclusion
The \(y\)-intercept of the line is \(8\).
Answer
What is the equation of the line that represents the scenario? Use the decimal value for slope.
Answered by
GPT-4o mini
Given that we've found the slope of the line to be \(-\frac{2}{5}\), we can convert this to decimal form:
\[
-\frac{2}{5} = -0.4
\]
Now, we have the slope \(m = -0.4\) and the \(y\)-intercept \(b = 8\). We can write the equation of the line using the slope-intercept form \(y = mx + b\):
\[
y = -0.4x + 8
\]
### Conclusion
The equation of the line that represents the scenario is:
\[
y = -0.4x + 8
\]
\[
-\frac{2}{5} = -0.4
\]
Now, we have the slope \(m = -0.4\) and the \(y\)-intercept \(b = 8\). We can write the equation of the line using the slope-intercept form \(y = mx + b\):
\[
y = -0.4x + 8
\]
### Conclusion
The equation of the line that represents the scenario is:
\[
y = -0.4x + 8
\]