Question
write the linear expression in the point interslope form for the line that passe through (-1,4) that has a slope of -1 dont give me the answer
Answers
Answer
am i right?
y=mx+c
Where
y=4
m=-1
x=-1
Then plug them in for c
4=1+c
Subtract 1 from both sides
c=3
In proper form it would be
y-4=-1(x–1)
And point intercept form it would be y=-1x+3
y=mx+c
Where
y=4
m=-1
x=-1
Then plug them in for c
4=1+c
Subtract 1 from both sides
c=3
In proper form it would be
y-4=-1(x–1)
And point intercept form it would be y=-1x+3
Answer
why is it not -1x instead of -x in slope intercept
Answer
so what exactly did i do wrong since i got the answers right
Answer
ok thanks for the feedback give me a similiar problem
Answer
is this righty-y1=m(x-x1)
y=mx+c
Point is (2,-3) slope is 4
So y=-3
m=4
x=2
So lets find c
y=mx+c
-3=4(2)+c
-3=8+c
Subtract 8 from both sides for c
5=c
Slope intercept form ends as y=4x+5
And point slope form ends as
Y-(-3)=4(x-2)
We can substitute since subtracting a negative is a positive
y+3=4(x-2)
y=mx+c
Point is (2,-3) slope is 4
So y=-3
m=4
x=2
So lets find c
y=mx+c
-3=4(2)+c
-3=8+c
Subtract 8 from both sides for c
5=c
Slope intercept form ends as y=4x+5
And point slope form ends as
Y-(-3)=4(x-2)
We can substitute since subtracting a negative is a positive
y+3=4(x-2)
Answered by
GPT-4o mini
To write the linear expression in point-slope form for a line, you use the formula:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.
In your case, the point given is \( (-1, 4) \) and the slope \( m \) is \( -1 \).
Now, you can substitute \( x_1 \), \( y_1 \), and \( m \) into the formula to find the point-slope form of the line. Replace \( x_1 \) with \(-1\), \( y_1 \) with \( 4\), and \( m \) with \(-1\).
After substituting, your expression will be ready in point-slope form!
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.
In your case, the point given is \( (-1, 4) \) and the slope \( m \) is \( -1 \).
Now, you can substitute \( x_1 \), \( y_1 \), and \( m \) into the formula to find the point-slope form of the line. Replace \( x_1 \) with \(-1\), \( y_1 \) with \( 4\), and \( m \) with \(-1\).
After substituting, your expression will be ready in point-slope form!
Answered by
GPT-4o mini
Let's clarify the process and the steps you've taken.
1. **Correct form of the line equation**: The point-slope form of the line is expressed as \(y - y_1 = m(x - x_1)\). If you want to express it in slope-intercept form, you use \(y = mx + c\).
2. **Given Point and Slope**:
- Point: \((-1, 4)\) implies \(x_1 = -1\) and \(y_1 = 4\).
- Slope: \(m = -1\).
3. **Point-Slope Form**:
Plugging the point and slope into the point-slope formula:
\[
y - 4 = -1(x + 1)
\]
(Note that it should be \((x + 1)\) since \(-1\) is used for \(x - (-1)\).)
4. **Solving for Slope-Intercept Form**:
To put it in slope-intercept form \(y = mx + c\), we will distribute and simplify:
\[
y - 4 = -1(x + 1)
\]
\[
y - 4 = -x - 1
\]
\[
y = -x - 1 + 4
\]
\[
y = -x + 3
\]
5. **Final Results**:
- The correct **point-slope form** is \(y - 4 = -1(x + 1)\).
- The correct **slope-intercept form** is \(y = -x + 3\).
So your overall process had the right intention, but there were some inaccuracies in plugging points into \(c\) and the expression form. Make sure to use the correct values when substituting, and you will arrive at the correct forms!
1. **Correct form of the line equation**: The point-slope form of the line is expressed as \(y - y_1 = m(x - x_1)\). If you want to express it in slope-intercept form, you use \(y = mx + c\).
2. **Given Point and Slope**:
- Point: \((-1, 4)\) implies \(x_1 = -1\) and \(y_1 = 4\).
- Slope: \(m = -1\).
3. **Point-Slope Form**:
Plugging the point and slope into the point-slope formula:
\[
y - 4 = -1(x + 1)
\]
(Note that it should be \((x + 1)\) since \(-1\) is used for \(x - (-1)\).)
4. **Solving for Slope-Intercept Form**:
To put it in slope-intercept form \(y = mx + c\), we will distribute and simplify:
\[
y - 4 = -1(x + 1)
\]
\[
y - 4 = -x - 1
\]
\[
y = -x - 1 + 4
\]
\[
y = -x + 3
\]
5. **Final Results**:
- The correct **point-slope form** is \(y - 4 = -1(x + 1)\).
- The correct **slope-intercept form** is \(y = -x + 3\).
So your overall process had the right intention, but there were some inaccuracies in plugging points into \(c\) and the expression form. Make sure to use the correct values when substituting, and you will arrive at the correct forms!
Answered by
GPT-4o mini
In the context of slope-intercept form, the general format is:
\[ y = mx + c \]
Where:
- \( m \) represents the slope,
- \( c \) represents the y-intercept, and
- \( x \) is the variable representing the x-coordinate.
In your case, we found that the slope \( m \) is \(-1\). When we write the equation in slope-intercept form, we should keep the negative sign associated with the slope.
So, when we substitute \( m = -1 \) into the slope-intercept form, it becomes:
\[ y = -1x + 3 \]
However, it's common to write \(-1x\) simply as \(-x\) for convenience. Both of these forms represent the same linear relationship:
- \( y = -1x + 3 \)
- \( y = -x + 3 \)
They are equivalent, and both convey that the slope is negative. So, both forms are valid; it's just a matter of preference in simplification and clarity.
\[ y = mx + c \]
Where:
- \( m \) represents the slope,
- \( c \) represents the y-intercept, and
- \( x \) is the variable representing the x-coordinate.
In your case, we found that the slope \( m \) is \(-1\). When we write the equation in slope-intercept form, we should keep the negative sign associated with the slope.
So, when we substitute \( m = -1 \) into the slope-intercept form, it becomes:
\[ y = -1x + 3 \]
However, it's common to write \(-1x\) simply as \(-x\) for convenience. Both of these forms represent the same linear relationship:
- \( y = -1x + 3 \)
- \( y = -x + 3 \)
They are equivalent, and both convey that the slope is negative. So, both forms are valid; it's just a matter of preference in simplification and clarity.
Answered by
GPT-4o mini
You did a lot of things correctly, and ultimately arrived at the correct answers for both forms of the linear equation! However, there were a few small misunderstandings and missteps in the way you articulated your process. Here are the key points:
1. **Substituting for \(c\)**:
You mentioned the equation \(y = mx + c\) and tried to find \(c\) by using the point \((x, y) = (-1, 4)\). However, when substituting for \(c\), you incorrectly placed the values. The correct way to determine \(c\) once you have the equation \(y = -x + c\) is to substitute the point into the equation:
\[
4 = -1(-1) + c \implies 4 = 1 + c \implies c = 3
\]
This means \(y = -x + 3\) is indeed correct.
2. **Point-Slope Form**:
When you wrote \(y - 4 = -1(x - 1)\), you mistakenly used \(x - 1\) instead of \(x + 1\). The correct point-slope form for the point \((-1, 4)\) should be:
\[
y - 4 = -1(x + 1)
\]
This implies that you use \(x - (-1)\) which simplifies to \(x + 1\).
3. **Slope-Intercept Form**:
When you derived the slope-intercept form from the correct point-slope form, you ultimately reached the right equation, \(y = -x + 3\), which effectively means your final form was indeed correct but you started with a slight error in the point-slope format.
In summary, while the final answers you provided were correct, addressing the minor issues in how you approached them in point-slope form and the substitution would help in clear communication and understanding of the process. Keep those points in mind, and overall, you did a great job!
1. **Substituting for \(c\)**:
You mentioned the equation \(y = mx + c\) and tried to find \(c\) by using the point \((x, y) = (-1, 4)\). However, when substituting for \(c\), you incorrectly placed the values. The correct way to determine \(c\) once you have the equation \(y = -x + c\) is to substitute the point into the equation:
\[
4 = -1(-1) + c \implies 4 = 1 + c \implies c = 3
\]
This means \(y = -x + 3\) is indeed correct.
2. **Point-Slope Form**:
When you wrote \(y - 4 = -1(x - 1)\), you mistakenly used \(x - 1\) instead of \(x + 1\). The correct point-slope form for the point \((-1, 4)\) should be:
\[
y - 4 = -1(x + 1)
\]
This implies that you use \(x - (-1)\) which simplifies to \(x + 1\).
3. **Slope-Intercept Form**:
When you derived the slope-intercept form from the correct point-slope form, you ultimately reached the right equation, \(y = -x + 3\), which effectively means your final form was indeed correct but you started with a slight error in the point-slope format.
In summary, while the final answers you provided were correct, addressing the minor issues in how you approached them in point-slope form and the substitution would help in clear communication and understanding of the process. Keep those points in mind, and overall, you did a great job!
Answered by
GPT-4o mini
Sure! Here’s a similar problem for you:
**Problem:** Write the linear expression in point-slope form for the line that passes through the point \( (2, -3) \) and has a slope of \( 4 \). Then convert it to slope-intercept form.
### Steps to Solve:
1. Use the point-slope form: \( y - y_1 = m(x - x_1) \).
2. Substitute the point \((x_1, y_1) = (2, -3)\) and \(m = 4\) into the formula.
3. Rearrange the equation to get it into slope-intercept form \(y = mx + c\).
### Give it a try!
**Problem:** Write the linear expression in point-slope form for the line that passes through the point \( (2, -3) \) and has a slope of \( 4 \). Then convert it to slope-intercept form.
### Steps to Solve:
1. Use the point-slope form: \( y - y_1 = m(x - x_1) \).
2. Substitute the point \((x_1, y_1) = (2, -3)\) and \(m = 4\) into the formula.
3. Rearrange the equation to get it into slope-intercept form \(y = mx + c\).
### Give it a try!
Answered by
GPT-4o mini
Let’s review your work step by step.
1. **Starting with the correct point-slope formula:**
You correctly wrote the point-slope form as:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1) = (2, -3)\) and \(m = 4\).
2. **Substituting into the point-slope form:**
Substituting the values gives:
\[
y - (-3) = 4(x - 2)
\]
Therefore, it simplifies to:
\[
y + 3 = 4(x - 2)
\]
This part is correct!
3. **Finding the slope-intercept form:**
Next, when you tried to find \(c\) using the slope-intercept form:
\[
y = mx + c
\]
you correctly started with the equation \(y = 4x + c\). However, when you substituted \(y = -3\) and \(x = 2\) to find \(c\), you inadvertently wrote \(c = 5\) instead of the correct arithmetic step.
Here’s how you should have derived \(c\):
\[
-3 = 4(2) + c
\]
\[
-3 = 8 + c
\]
Subtract \(8\) from both sides:
\[
-3 - 8 = c \implies c = -11
\]
So, the correct slope-intercept form would be:
\[
y = 4x - 11
\]
### Summary of Results:
- **Point-Slope Form**: \(y + 3 = 4(x - 2)\)
- **Slope-Intercept Form**: \(y = 4x - 11\)
You did well in recognizing the formulas and setting things up! The mistake occurred in finding \(c\). Be sure to double-check your arithmetic steps, and keep practicing!
1. **Starting with the correct point-slope formula:**
You correctly wrote the point-slope form as:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1) = (2, -3)\) and \(m = 4\).
2. **Substituting into the point-slope form:**
Substituting the values gives:
\[
y - (-3) = 4(x - 2)
\]
Therefore, it simplifies to:
\[
y + 3 = 4(x - 2)
\]
This part is correct!
3. **Finding the slope-intercept form:**
Next, when you tried to find \(c\) using the slope-intercept form:
\[
y = mx + c
\]
you correctly started with the equation \(y = 4x + c\). However, when you substituted \(y = -3\) and \(x = 2\) to find \(c\), you inadvertently wrote \(c = 5\) instead of the correct arithmetic step.
Here’s how you should have derived \(c\):
\[
-3 = 4(2) + c
\]
\[
-3 = 8 + c
\]
Subtract \(8\) from both sides:
\[
-3 - 8 = c \implies c = -11
\]
So, the correct slope-intercept form would be:
\[
y = 4x - 11
\]
### Summary of Results:
- **Point-Slope Form**: \(y + 3 = 4(x - 2)\)
- **Slope-Intercept Form**: \(y = 4x - 11\)
You did well in recognizing the formulas and setting things up! The mistake occurred in finding \(c\). Be sure to double-check your arithmetic steps, and keep practicing!