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
y=56x+6
y equals Start Fraction 5 over 6 End Fraction x plus 6
6y=5x
6 y equals 5 x
y=−65x+6
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
y=56x+6
y equals Start Fraction 5 over 6 End Fraction x plus 6
6y=5x
6 y equals 5 x
y=−65x+6
Answers
GPT-4o mini
To find a line parallel to \( y = 56x \) that passes through the point \( (12, 6) \), we note that parallel lines have the same slope.
The slope of the line \( y = 56x \) is 56. Thus, the line we are looking for will also have a slope of 56 and can be represented in the slope-intercept form, \( y = mx + b \), where \( m \) is the slope.
To find the y-intercept \( b \), we can use the point \( (12, 6) \) in the equation:
\[
y = 56x + b
\]
Substituting in the point \( (12, 6) \):
\[
6 = 56(12) + b
\]
\[
6 = 672 + b
\]
\[
b = 6 - 672
\]
\[
b = -666
\]
So, the equation of the line that is parallel to \( y = 56x \) and passes through the point \( (12, 6) \) is:
\[
y = 56x - 666
\]
None of your provided options match this equation. Therefore, it seems there may be an issue with the options given. The correct line based on the criteria we solved is indeed \( y = 56x - 666 \).
The slope of the line \( y = 56x \) is 56. Thus, the line we are looking for will also have a slope of 56 and can be represented in the slope-intercept form, \( y = mx + b \), where \( m \) is the slope.
To find the y-intercept \( b \), we can use the point \( (12, 6) \) in the equation:
\[
y = 56x + b
\]
Substituting in the point \( (12, 6) \):
\[
6 = 56(12) + b
\]
\[
6 = 672 + b
\]
\[
b = 6 - 672
\]
\[
b = -666
\]
So, the equation of the line that is parallel to \( y = 56x \) and passes through the point \( (12, 6) \) is:
\[
y = 56x - 666
\]
None of your provided options match this equation. Therefore, it seems there may be an issue with the options given. The correct line based on the criteria we solved is indeed \( y = 56x - 666 \).