Question
Which line is parallel to the line y=56x and goes through the point (12,6) ?(1 point) Responses y=56x−4 y equals Start Fraction 5 over 6 End Fraction x minus 4 6y=5x 6 y equals 5 x y=56x+6 y equals Start Fraction 5 over 6 End Fraction x plus 6 y=−65x+6
Answers
Answer
GIVE ME ANSAWER
Answered by
GPT-4o mini
To find a line that is parallel to \( y = 56x \) and passes through the point \( (12, 6) \), we need to first identify the slope of the given line. The line \( y = 56x \) has a slope of \( 56 \).
Parallel lines have the same slope, so the slope of the line we are looking for is also \( 56 \). We can use the point-slope form of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope.
Given the point \( (12, 6) \) and the slope \( 56 \):
\[
y - 6 = 56(x - 12)
\]
Now, we can expand this equation:
\[
y - 6 = 56x - 672
\]
\[
y = 56x - 672 + 6
\]
\[
y = 56x - 666
\]
Now we will compare this with the provided options to see if any line has this slope of 56 and passes through the point.
None of the given options \( y = 56x - 4 \), \( y = \frac{5}{6}x - 4 \), \( 6y = 5x \), \( y = 56x + 6 \), \( y = \frac{5}{6}x + 6 \), \( y = -65x + 6 \) are equivalent to \( y = 56x - 666 \) or have the same slope of \( 56 \).
It seems none of the options exactly match our derived equation, since they either have a different slope or just incorrect intercept values.
However, if we calculate the necessary slope and try to identify if any of them represent a parallel line with the correct modifications, the right choice will reflect our slope but not through \( (12, 6) \):
Thus, the line parallel to \( y = 56x \) that goes through the point \( (12, 6) \) that we calculated is not among the provided options.
Therefore, please check if any of the options are modified forms or adjustments of our calculated output or consider that none may be correct as phrased.
Parallel lines have the same slope, so the slope of the line we are looking for is also \( 56 \). We can use the point-slope form of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope.
Given the point \( (12, 6) \) and the slope \( 56 \):
\[
y - 6 = 56(x - 12)
\]
Now, we can expand this equation:
\[
y - 6 = 56x - 672
\]
\[
y = 56x - 672 + 6
\]
\[
y = 56x - 666
\]
Now we will compare this with the provided options to see if any line has this slope of 56 and passes through the point.
None of the given options \( y = 56x - 4 \), \( y = \frac{5}{6}x - 4 \), \( 6y = 5x \), \( y = 56x + 6 \), \( y = \frac{5}{6}x + 6 \), \( y = -65x + 6 \) are equivalent to \( y = 56x - 666 \) or have the same slope of \( 56 \).
It seems none of the options exactly match our derived equation, since they either have a different slope or just incorrect intercept values.
However, if we calculate the necessary slope and try to identify if any of them represent a parallel line with the correct modifications, the right choice will reflect our slope but not through \( (12, 6) \):
Thus, the line parallel to \( y = 56x \) that goes through the point \( (12, 6) \) that we calculated is not among the provided options.
Therefore, please check if any of the options are modified forms or adjustments of our calculated output or consider that none may be correct as phrased.
Answered by
GPT-4o mini
The line that is parallel to \( y = 56x \) and goes through the point \( (12, 6) \) is:
**None of the provided options are correct.**
However, the equation of the parallel line you could derive is \( y = 56x - 666 \) which does not match any of the options given.
If you meant to ask for the right answer from the options provided, the closest option with the correct slope should still maintain \( y = 56x \) slope, but confirming any choices was unfruitful.
Apologies for the confusion; can you clarify if you need a specific answer from given options, or if those options are absolved?
**None of the provided options are correct.**
However, the equation of the parallel line you could derive is \( y = 56x - 666 \) which does not match any of the options given.
If you meant to ask for the right answer from the options provided, the closest option with the correct slope should still maintain \( y = 56x \) slope, but confirming any choices was unfruitful.
Apologies for the confusion; can you clarify if you need a specific answer from given options, or if those options are absolved?