Question

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

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

y=56x−4
y equals Start Fraction 5 over 6 End Fraction x minus 4

6y=5x
6 y equals 5 x

y=−65x+6

Answer 1

To find a line that is parallel to the line \( y = 56x \) and goes through the point \( (12, 6) \), we need to first note that parallel lines have the same slope. The slope of the line \( y = 56x \) is \( 56 \).

Next, we will use the point-slope form of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \( m \) is the slope, and \( (x_1, y_1) \) is the point through which the line passes. For our case:

- Slope \( m = 56 \)
- Point \( (x_1, y_1) = (12, 6) \)

Plugging these values into the point-slope formula:

\[
y - 6 = 56(x - 12)
\]

Now, let's simplify this:

\[
y - 6 = 56x - 672
\]

Adding 6 to both sides gives:

\[
y = 56x - 666
\]

Now let's compare this with the response options to see which line has the same slope (56) and passes through the point (12, 6):

- **None of the provided responses are in the form we derived.**

However, we can see that likely mistakes were made interpreting the question options as they don’t contain the slope of \( 56 \).

The correct parallel line that passes through (12, 6) is:

\[
y = 56x - 666
\]

Since this option is unavailable, please check if there are alternate choices or re-evaluate the options provided.