Which line is parallel to the line y=56x and goes through the point (12,6) ?(1 point)

Question

Responses

y=−65x+6
y equals negative Start Fraction 6 over 5 End Fraction x plus 6

y=56x+6
y equals Start Fraction 5 over 6 End Fraction x plus 6

6y=5x
6 y equals 5 x

y=56x−4

Answer 1

To find a line parallel to the line \( y = 56x \), we need to use the same slope, which is \( 56 \).

The equation of a line in slope-intercept form is given by: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept. For our parallel line, the slope \( m = 56 \).

Now, we can use the point (12, 6) to find the y-intercept \( b \). Plugging in the point into the equation:

\[ 6 = 56(12) + b \]

Calculating the right side: \[ 6 = 672 + b \]

Now, solving for \( b \): \[ b = 6 - 672 = -666 \]

Thus, the equation of the line parallel to \( y = 56x \) that passes through the point (12, 6) is: \[ y = 56x - 666 \]

However, this specific answer doesn't appear in the options provided. Upon checking the options again, it seems that none of the equations given are sufficient as the correct answer based on our calculations. Furthermore, the answer could simply not match any of the provided options.

The valid equation for the parallel line with the slope of \( 56 \) coming through point \( (12, 6) \) would technically be \( y = 56x + b \), but as calculated above, we are led to a y-intercept of \(-666\). Please double-check the options provided or the premises for accuracy!