Question
write he linear equation in the point slope formfor the line that passes through (-1,4) and has a slope of -1
Answers
Answer
thats a lie tell me the actual answer
Answer
give me a similiar problem
Answer
tell me if im right y=mx+c where y=-3
m is 4 x is 2 and c is -11 for the ending of -3=8+c
m is 4 x is 2 and c is -11 for the ending of -3=8+c
Answer
give me another similiar problem
Answer
am i right? y=mx+c
m=-2
x=3
y=5
So
5=-2(3)+c
5=-6+c
Add 6 to both sides
11=c
So in slope intercept form y=-2x+11
m=-2
x=3
y=5
So
5=-2(3)+c
5=-6+c
Add 6 to both sides
11=c
So in slope intercept form y=-2x+11
Answered by
GPT-4o mini
To write the linear equation in point-slope form for a line that passes through the point \((-1, 4)\) and has a slope of \(-1\), we use the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through.
Here, \(m = -1\), \(x_1 = -1\), and \(y_1 = 4\). Plugging these values into the formula gives:
\[
y - 4 = -1(x - (-1))
\]
This simplifies to:
\[
y - 4 = -1(x + 1)
\]
So, the point-slope form of the equation of the line is:
\[
y - 4 = -1(x + 1)
\]
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through.
Here, \(m = -1\), \(x_1 = -1\), and \(y_1 = 4\). Plugging these values into the formula gives:
\[
y - 4 = -1(x - (-1))
\]
This simplifies to:
\[
y - 4 = -1(x + 1)
\]
So, the point-slope form of the equation of the line is:
\[
y - 4 = -1(x + 1)
\]
Answered by
GPT-4o mini
I apologize for any confusion. Let's correctly derive the equation step by step.
To write the equation of a line in point-slope form, we use the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
where:
- \((x_1, y_1)\) is a point on the line,
- \(m\) is the slope of the line.
Given:
- Point \((-1, 4)\) implies \(x_1 = -1\) and \(y_1 = 4\),
- Slope \(m = -1\).
Substituting these values into the point-slope formula:
\[
y - 4 = -1(x - (-1))
\]
This simplifies to:
\[
y - 4 = -1(x + 1)
\]
Rearranging gives:
\[
y - 4 = -x - 1
\]
And then,
\[
y = -x + 3
\]
So the point-slope form of the equation is correctly stated as:
\[
y - 4 = -1(x + 1)
\]
Thank you for your patience, and if you have further questions or need clarification, feel free to ask!
To write the equation of a line in point-slope form, we use the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
where:
- \((x_1, y_1)\) is a point on the line,
- \(m\) is the slope of the line.
Given:
- Point \((-1, 4)\) implies \(x_1 = -1\) and \(y_1 = 4\),
- Slope \(m = -1\).
Substituting these values into the point-slope formula:
\[
y - 4 = -1(x - (-1))
\]
This simplifies to:
\[
y - 4 = -1(x + 1)
\]
Rearranging gives:
\[
y - 4 = -x - 1
\]
And then,
\[
y = -x + 3
\]
So the point-slope form of the equation is correctly stated as:
\[
y - 4 = -1(x + 1)
\]
Thank you for your patience, and if you have further questions or need clarification, feel free to ask!
Answered by
GPT-4o mini
Sure! Here’s a similar problem for you to solve:
**Problem:** Write the linear equation in point-slope form for the line that passes through the point \((2, -3)\) and has a slope of \(4\).
Once you have your answer, I can help check it!
**Problem:** Write the linear equation in point-slope form for the line that passes through the point \((2, -3)\) and has a slope of \(4\).
Once you have your answer, I can help check it!
Answered by
GPT-4o mini
It looks like you're trying to find the y-intercept \(c\) in the slope-intercept form \(y = mx + c\), which is a different approach than using point-slope form. Let's clarify both methods.
### Point-Slope Form
1. Using the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1) = (2, -3)\) and \(m = 4\):
\[
y - (-3) = 4(x - 2)
\]
This simplifies to:
\[
y + 3 = 4(x - 2)
\]
Which means:
\[
y + 3 = 4x - 8
\]
Therefore, the point-slope form is:
\[
y + 3 = 4(x - 2)
\]
### Slope-Intercept Form
If you want to express it in slope-intercept form \(y = mx + c\):
1. From the previous step, after simplifying \((y + 3 = 4x - 8)\):
\[
y = 4x - 8 - 3
\]
This simplifies to:
\[
y = 4x - 11
\]
Thus, in slope-intercept form, the equation is:
\[
y = 4x - 11
\]
### Summary
- The equation in **point-slope form** is \(y + 3 = 4(x - 2)\).
- The equation in **slope-intercept form** is \(y = 4x - 11\).
In your message, you mentioned finding \(c\), but be sure you're clear about whether you're looking for the equation in point-slope form or putting it in slope-intercept form. Let me know if this helps or if you have any further questions!
### Point-Slope Form
1. Using the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1) = (2, -3)\) and \(m = 4\):
\[
y - (-3) = 4(x - 2)
\]
This simplifies to:
\[
y + 3 = 4(x - 2)
\]
Which means:
\[
y + 3 = 4x - 8
\]
Therefore, the point-slope form is:
\[
y + 3 = 4(x - 2)
\]
### Slope-Intercept Form
If you want to express it in slope-intercept form \(y = mx + c\):
1. From the previous step, after simplifying \((y + 3 = 4x - 8)\):
\[
y = 4x - 8 - 3
\]
This simplifies to:
\[
y = 4x - 11
\]
Thus, in slope-intercept form, the equation is:
\[
y = 4x - 11
\]
### Summary
- The equation in **point-slope form** is \(y + 3 = 4(x - 2)\).
- The equation in **slope-intercept form** is \(y = 4x - 11\).
In your message, you mentioned finding \(c\), but be sure you're clear about whether you're looking for the equation in point-slope form or putting it in slope-intercept form. Let me know if this helps or if you have any further questions!
Answered by
GPT-4o mini
Sure! Here’s another similar problem for you to solve:
**Problem:** Write the linear equation in point-slope form for the line that passes through the point \((3, 5)\) and has a slope of \(-2\).
Give it a try, and I'll be here to check your work!
**Problem:** Write the linear equation in point-slope form for the line that passes through the point \((3, 5)\) and has a slope of \(-2\).
Give it a try, and I'll be here to check your work!
Answered by
GPT-4o mini
Your calculations for finding the slope-intercept form are correct! Here's a breakdown of what you did:
### Started with the Slope-Intercept Form
You used the equation:
\[
y = mx + c
\]
and substituted the values:
- \(m = -2\)
- \(x = 3\)
- \(y = 5\)
You set it up like this:
\[
5 = -2(3) + c
\]
Then you simplified:
\[
5 = -6 + c
\]
Adding \(6\) to both sides gives:
\[
11 = c
\]
So you found:
\[
c = 11
\]
### Slope-Intercept Form
Now, the slope-intercept form of the line is:
\[
y = -2x + 11
\]
### Point-Slope Form
However, the original problem asked for the equation in **point-slope form**. The point-slope form for the point \((3, 5)\) and slope \(-2\) would be:
\[
y - y_1 = m(x - x_1)
\]
Substituting the values:
\[
y - 5 = -2(x - 3)
\]
You could simplify that, but you correctly found the slope-intercept form.
### Conclusion
So, while your slope-intercept form \(y = -2x + 11\) is correct, the point-slope form would be:
\[
y - 5 = -2(x - 3)
\]
If you need another problem or further clarification, just let me know!
### Started with the Slope-Intercept Form
You used the equation:
\[
y = mx + c
\]
and substituted the values:
- \(m = -2\)
- \(x = 3\)
- \(y = 5\)
You set it up like this:
\[
5 = -2(3) + c
\]
Then you simplified:
\[
5 = -6 + c
\]
Adding \(6\) to both sides gives:
\[
11 = c
\]
So you found:
\[
c = 11
\]
### Slope-Intercept Form
Now, the slope-intercept form of the line is:
\[
y = -2x + 11
\]
### Point-Slope Form
However, the original problem asked for the equation in **point-slope form**. The point-slope form for the point \((3, 5)\) and slope \(-2\) would be:
\[
y - y_1 = m(x - x_1)
\]
Substituting the values:
\[
y - 5 = -2(x - 3)
\]
You could simplify that, but you correctly found the slope-intercept form.
### Conclusion
So, while your slope-intercept form \(y = -2x + 11\) is correct, the point-slope form would be:
\[
y - 5 = -2(x - 3)
\]
If you need another problem or further clarification, just let me know!
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