Question
Slope and Intercept
y - 1/2 ( x - 8)
y - 1/2 ( x - 8)
Answers
Answer
How about
y = 3/2x + 1
y = 3/2x + 1
Answer
what about y = 5
what about y = -7
what about y = -7
Answer
how awbout
y = -x + 3
y = -x + 3
Answer
how about y = 6x - 13
Answered by
GPT-4o mini
To express the equation in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), we need to rearrange the given equation \(y - \frac{1}{2}(x - 8)\).
Starting with the given equation:
\[
y - \frac{1}{2}(x - 8)
\]
We can distribute \(-\frac{1}{2}\) over \((x - 8)\):
\[
y - \frac{1}{2}x + \frac{1}{2} \cdot 8
\]
This simplifies to:
\[
y - \frac{1}{2}x + 4
\]
Now, add \(\frac{1}{2}x\) to both sides to isolate \(y\):
\[
y = \frac{1}{2}x - 4 + 4
\]
Simplifying gives us:
\[
y = \frac{1}{2}x + 4
\]
So, in slope-intercept form, the equation is:
\[
y = \frac{1}{2}x + 4
\]
- Slope (\(m\)) = \(\frac{1}{2}\)
- Y-intercept (\(b\)) = \(4\)
Starting with the given equation:
\[
y - \frac{1}{2}(x - 8)
\]
We can distribute \(-\frac{1}{2}\) over \((x - 8)\):
\[
y - \frac{1}{2}x + \frac{1}{2} \cdot 8
\]
This simplifies to:
\[
y - \frac{1}{2}x + 4
\]
Now, add \(\frac{1}{2}x\) to both sides to isolate \(y\):
\[
y = \frac{1}{2}x - 4 + 4
\]
Simplifying gives us:
\[
y = \frac{1}{2}x + 4
\]
So, in slope-intercept form, the equation is:
\[
y = \frac{1}{2}x + 4
\]
- Slope (\(m\)) = \(\frac{1}{2}\)
- Y-intercept (\(b\)) = \(4\)
Answered by
GPT-4o mini
The equation you provided is already in slope-intercept form, which is given by the equation \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
For the equation:
\[
y = \frac{3}{2}x + 1
\]
- **Slope (\(m\))**: \(\frac{3}{2}\)
- **Y-intercept (\(b\))**: \(1\)
This means that the slope of the line is \(\frac{3}{2}\), indicating that for every increase of 1 in \(x\), \(y\) increases by \(\frac{3}{2}\). The line crosses the y-axis at the point \((0, 1)\).
For the equation:
\[
y = \frac{3}{2}x + 1
\]
- **Slope (\(m\))**: \(\frac{3}{2}\)
- **Y-intercept (\(b\))**: \(1\)
This means that the slope of the line is \(\frac{3}{2}\), indicating that for every increase of 1 in \(x\), \(y\) increases by \(\frac{3}{2}\). The line crosses the y-axis at the point \((0, 1)\).
Answered by
GPT-4o mini
The equations \(y = 5\) and \(y = -7\) represent horizontal lines.
### For \(y = 5\):
- **Slope (\(m\))**: 0 (the line is horizontal)
- **Y-intercept (\(b\))**: 5 (the line crosses the y-axis at (0, 5))
### For \(y = -7\):
- **Slope (\(m\))**: 0 (again, the line is horizontal)
- **Y-intercept (\(b\))**: -7 (the line crosses the y-axis at (0, -7))
### Summary:
- Both lines have a slope of 0, indicating they are horizontal.
- \(y = 5\) is a horizontal line that is 5 units above the x-axis.
- \(y = -7\) is a horizontal line that is 7 units below the x-axis.
### For \(y = 5\):
- **Slope (\(m\))**: 0 (the line is horizontal)
- **Y-intercept (\(b\))**: 5 (the line crosses the y-axis at (0, 5))
### For \(y = -7\):
- **Slope (\(m\))**: 0 (again, the line is horizontal)
- **Y-intercept (\(b\))**: -7 (the line crosses the y-axis at (0, -7))
### Summary:
- Both lines have a slope of 0, indicating they are horizontal.
- \(y = 5\) is a horizontal line that is 5 units above the x-axis.
- \(y = -7\) is a horizontal line that is 7 units below the x-axis.
Answered by
GPT-4o mini
The equation \(y = -x + 3\) is already in slope-intercept form, which is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
### For the equation \(y = -x + 3\):
- **Slope (\(m\))**: \(-1\) (This means that for every increase of 1 in \(x\), \(y\) decreases by 1.)
- **Y-intercept (\(b\))**: \(3\) (The point where the line crosses the y-axis is at (0, 3).)
### Summary:
- The slope of the line is \(-1\), indicating a downward slope.
- The line crosses the y-axis at the point \((0, 3)\).
### For the equation \(y = -x + 3\):
- **Slope (\(m\))**: \(-1\) (This means that for every increase of 1 in \(x\), \(y\) decreases by 1.)
- **Y-intercept (\(b\))**: \(3\) (The point where the line crosses the y-axis is at (0, 3).)
### Summary:
- The slope of the line is \(-1\), indicating a downward slope.
- The line crosses the y-axis at the point \((0, 3)\).
Answered by
GPT-4o mini
The equation \(y = 6x - 13\) is already in slope-intercept form, which is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
### For the equation \(y = 6x - 13\):
- **Slope (\(m\))**: \(6\) (This means that for every increase of 1 in \(x\), \(y\) increases by \(6\).)
- **Y-intercept (\(b\))**: \(-13\) (The point where the line crosses the y-axis is at \((0, -13)\).)
### Summary:
- The slope of the line is \(6\), indicating a steep upward slope.
- The line crosses the y-axis at the point \((0, -13)\).
### For the equation \(y = 6x - 13\):
- **Slope (\(m\))**: \(6\) (This means that for every increase of 1 in \(x\), \(y\) increases by \(6\).)
- **Y-intercept (\(b\))**: \(-13\) (The point where the line crosses the y-axis is at \((0, -13)\).)
### Summary:
- The slope of the line is \(6\), indicating a steep upward slope.
- The line crosses the y-axis at the point \((0, -13)\).