Question
10 of 18
A line passes through the point (-7, 5) and has a slope of. Which is another point that the line passes through?
NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.
(1 point)
Ο (-9, 2)
Ο (-2, 9)
(9,2)
(2,0)
A line passes through the point (-7, 5) and has a slope of. Which is another point that the line passes through?
NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.
(1 point)
Ο (-9, 2)
Ο (-2, 9)
(9,2)
(2,0)
Answers
GPT-4o mini
To find another point on the line that passes through the point (-7, 5) with a given slope \( m \), we can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
In this case, \( (x_1, y_1) = (-7, 5) \).
Assuming the slope is \( m \), the equation of the line would be:
\[ y - 5 = m(x + 7) \]
To find another point, we can choose a value for \( x \), solve for \( y \), and then see if this point corresponds to any of the options given.
However, the problem states "has a slope of" but does not provide a specific numeric value for the slope \( m \), making it impossible to calculate the exact coordinates of another point without that information.
What we can do instead is check each of the options provided to see which one satisfies the relationship dictated by the current slope (if we had it).
Let's evaluate each option assuming different \( m \) values if \( m \) were to be defined.
1. **For (-9, 2):**
\[ y - 5 = m(x + 7) \]
Substituting the point (-9, 2):
\[ 2 - 5 = m(-9 + 7) \]
\[ -3 = m(-2) \]
\[ m = \frac{3}{2} \]
2. **For (-2, 9):**
Substituting the point (-2, 9):
\[ 9 - 5 = m(-2 + 7) \]
\[ 4 = m(5) \]
\[ m = \frac{4}{5} \]
3. **For (9, 2):**
Substituting the point (9, 2):
\[ 2 - 5 = m(9 + 7) \]
\[ -3 = m(16) \]
\[ m = -\frac{3}{16} \]
4. **For (2, 0):**
Substituting the point (2, 0):
\[ 0 - 5 = m(2 + 7) \]
\[ -5 = m(9) \]
\[ m = -\frac{5}{9} \]
Without knowing the original slope \( m \), we cannot definitively say which options are correct.
You should select the option based on any provided slope or more information that you have regarding the slope that will allow you to identify which point fits or if they don't correspond to the slope provided.
If I had to make a suggestion, I would say go through these options to check if any had been explicitly instructed with a numerical slope value. Careful checking through your problem statement again should clarify further, or you may apply the slopes calculated here to find which fits best!
\[ y - y_1 = m(x - x_1) \]
In this case, \( (x_1, y_1) = (-7, 5) \).
Assuming the slope is \( m \), the equation of the line would be:
\[ y - 5 = m(x + 7) \]
To find another point, we can choose a value for \( x \), solve for \( y \), and then see if this point corresponds to any of the options given.
However, the problem states "has a slope of" but does not provide a specific numeric value for the slope \( m \), making it impossible to calculate the exact coordinates of another point without that information.
What we can do instead is check each of the options provided to see which one satisfies the relationship dictated by the current slope (if we had it).
Let's evaluate each option assuming different \( m \) values if \( m \) were to be defined.
1. **For (-9, 2):**
\[ y - 5 = m(x + 7) \]
Substituting the point (-9, 2):
\[ 2 - 5 = m(-9 + 7) \]
\[ -3 = m(-2) \]
\[ m = \frac{3}{2} \]
2. **For (-2, 9):**
Substituting the point (-2, 9):
\[ 9 - 5 = m(-2 + 7) \]
\[ 4 = m(5) \]
\[ m = \frac{4}{5} \]
3. **For (9, 2):**
Substituting the point (9, 2):
\[ 2 - 5 = m(9 + 7) \]
\[ -3 = m(16) \]
\[ m = -\frac{3}{16} \]
4. **For (2, 0):**
Substituting the point (2, 0):
\[ 0 - 5 = m(2 + 7) \]
\[ -5 = m(9) \]
\[ m = -\frac{5}{9} \]
Without knowing the original slope \( m \), we cannot definitively say which options are correct.
You should select the option based on any provided slope or more information that you have regarding the slope that will allow you to identify which point fits or if they don't correspond to the slope provided.
If I had to make a suggestion, I would say go through these options to check if any had been explicitly instructed with a numerical slope value. Careful checking through your problem statement again should clarify further, or you may apply the slopes calculated here to find which fits best!