Question
What is the slope and the y -intercept of the equation 9+272x=−32y . Write the y -intercept as an ordered pair.(1 point) The slope is BLANK . The y -intercept is (BLANK ).
Answers
Answer
wrong
Answer
everything there is wrong. its not 8.5 nor 9/32
Answered by
GPT-4o mini
To find the slope and the y-intercept of the equation \(9 + 272x = -32y\), we first need to rearrange it into the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the given equation:
\[
9 + 272x = -32y
\]
We can move \(9\) and \(272x\) to the other side:
\[
-32y = -272x - 9
\]
Next, we divide every term by \(-32\):
\[
y = \frac{272}{32}x + \frac{9}{32}
\]
Now, simplify \(\frac{272}{32}\):
\[
\frac{272}{32} = 8.5
\]
So the equation in slope-intercept form is:
\[
y = 8.5x + \frac{9}{32}
\]
From this, we find:
- The slope \(m\) is \(8.5\).
- The y-intercept \(b\) is \(\frac{9}{32}\).
Now, expressing the y-intercept as an ordered pair (where \(x=0\)) gives us:
\[
(0, \frac{9}{32})
\]
Thus, the final answers are:
- The slope is **8.5**.
- The y-intercept is **(0, \frac{9}{32})**.
Starting with the given equation:
\[
9 + 272x = -32y
\]
We can move \(9\) and \(272x\) to the other side:
\[
-32y = -272x - 9
\]
Next, we divide every term by \(-32\):
\[
y = \frac{272}{32}x + \frac{9}{32}
\]
Now, simplify \(\frac{272}{32}\):
\[
\frac{272}{32} = 8.5
\]
So the equation in slope-intercept form is:
\[
y = 8.5x + \frac{9}{32}
\]
From this, we find:
- The slope \(m\) is \(8.5\).
- The y-intercept \(b\) is \(\frac{9}{32}\).
Now, expressing the y-intercept as an ordered pair (where \(x=0\)) gives us:
\[
(0, \frac{9}{32})
\]
Thus, the final answers are:
- The slope is **8.5**.
- The y-intercept is **(0, \frac{9}{32})**.
Answered by
GPT-4o mini
I apologize for any inaccuracies. Let's go through the process again step by step.
Starting with the equation:
\[
9 + 272x = -32y
\]
We need to solve for \(y\) by isolating it on one side. First, we rearrange the equation:
\[
-32y = -272x - 9
\]
Now, divide by \(-32\) to solve for \(y\):
\[
y = \frac{272}{32}x + \frac{9}{32}
\]
Now let's simplify \(\frac{272}{32}\):
\[
\frac{272}{32} = 8.5
\]
This gives us the equation in slope-intercept form:
\[
y = 8.5x + \frac{9}{32}
\]
Thus:
- The slope \(m\) is **\(\frac{272}{32} = 8.5\)**.
- The y-intercept \(b\) is **\(\frac{9}{32}\)**.
The y-intercept as an ordered pair is:
\[
\left(0, \frac{9}{32}\right)
\]
To summarize:
- The slope is **8.5**.
- The y-intercept is **(0, \frac{9}{32})**.
If there are specific aspects of the calculations you would like clarification on or if there's a particular error you believe I've made, please let me know!
Starting with the equation:
\[
9 + 272x = -32y
\]
We need to solve for \(y\) by isolating it on one side. First, we rearrange the equation:
\[
-32y = -272x - 9
\]
Now, divide by \(-32\) to solve for \(y\):
\[
y = \frac{272}{32}x + \frac{9}{32}
\]
Now let's simplify \(\frac{272}{32}\):
\[
\frac{272}{32} = 8.5
\]
This gives us the equation in slope-intercept form:
\[
y = 8.5x + \frac{9}{32}
\]
Thus:
- The slope \(m\) is **\(\frac{272}{32} = 8.5\)**.
- The y-intercept \(b\) is **\(\frac{9}{32}\)**.
The y-intercept as an ordered pair is:
\[
\left(0, \frac{9}{32}\right)
\]
To summarize:
- The slope is **8.5**.
- The y-intercept is **(0, \frac{9}{32})**.
If there are specific aspects of the calculations you would like clarification on or if there's a particular error you believe I've made, please let me know!
Answered by
GPT-4o mini
I apologize for the mistakes in my previous calculations. Let's go through the problem step by step again.
The equation we start with is:
\[
9 + 272x = -32y
\]
To find the slope and y-intercept, we first need to rearrange the equation into slope-intercept form \(y = mx + b\).
1. **Move the terms around to get \(y\) by itself**:
Start by subtracting \(272x\) from both sides:
\[
-32y = -272x - 9
\]
2. **Next, divide everything by -32** to isolate \(y\):
\[
y = \frac{272}{32}x + \frac{9}{32}
\]
3. **Simplify \(\frac{272}{32}\) and \(\frac{9}{32}\)**:
Let's simplify \(\frac{272}{32}\):
\[
\frac{272 \div 16}{32 \div 16} = \frac{17}{2} \quad (\text{which is } 8.5\text{ as a decimal})
\]
However, let's keep it as a fraction:
\[
y = \frac{17}{2}x + \frac{9}{32}
\]
4. **Identify the slope and y-intercept**:
- The slope \(m\) is \(\frac{17}{2}\).
- The y-intercept \(b\) is \(\frac{9}{32}\).
5. **Write down the y-intercept as an ordered pair**:
The y-intercept is when \(x = 0\):
\[
\left(0, \frac{9}{32}\right)
\]
To summarize:
- The slope is **\(\frac{17}{2}\)**.
- The y-intercept is **\(\left(0, \frac{9}{32}\right)\)**.
Thank you for your patience, and I apologize for the previous errors.
The equation we start with is:
\[
9 + 272x = -32y
\]
To find the slope and y-intercept, we first need to rearrange the equation into slope-intercept form \(y = mx + b\).
1. **Move the terms around to get \(y\) by itself**:
Start by subtracting \(272x\) from both sides:
\[
-32y = -272x - 9
\]
2. **Next, divide everything by -32** to isolate \(y\):
\[
y = \frac{272}{32}x + \frac{9}{32}
\]
3. **Simplify \(\frac{272}{32}\) and \(\frac{9}{32}\)**:
Let's simplify \(\frac{272}{32}\):
\[
\frac{272 \div 16}{32 \div 16} = \frac{17}{2} \quad (\text{which is } 8.5\text{ as a decimal})
\]
However, let's keep it as a fraction:
\[
y = \frac{17}{2}x + \frac{9}{32}
\]
4. **Identify the slope and y-intercept**:
- The slope \(m\) is \(\frac{17}{2}\).
- The y-intercept \(b\) is \(\frac{9}{32}\).
5. **Write down the y-intercept as an ordered pair**:
The y-intercept is when \(x = 0\):
\[
\left(0, \frac{9}{32}\right)
\]
To summarize:
- The slope is **\(\frac{17}{2}\)**.
- The y-intercept is **\(\left(0, \frac{9}{32}\right)\)**.
Thank you for your patience, and I apologize for the previous errors.