Question

Which line is parallel to the line y=5/6x
and goes through the point (12,6)
?(1 point)
Responses

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

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

6y=5x
6 y equals 5 x

y=−6/5x+6

Answer 1

To find a line that is parallel to the line \( y = \frac{5}{6}x \) and goes through the point \( (12, 6) \), we need to remember that parallel lines have the same slope.

The slope of the given line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \). We will use this slope to find the equation of our parallel line that passes through the point \( (12, 6) \).

We can use the point-slope form of the equation of a line:

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

where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through. Here, \( m = \frac{5}{6} \), \( x_1 = 12 \), and \( y_1 = 6 \).

Substituting these values into the point-slope equation:

\[
y - 6 = \frac{5}{6}(x - 12)
\]

Now, we can distribute \( \frac{5}{6} \):

\[
y - 6 = \frac{5}{6}x - \frac{5}{6} \cdot 12
\]
\[
y - 6 = \frac{5}{6}x - 10
\]

Next, add 6 to both sides to solve for \( y \):

\[
y = \frac{5}{6}x - 10 + 6
\]
\[
y = \frac{5}{6}x - 4
\]

Now, we need to check which option corresponds to this equation.

The correct choice is:

**y = \(\frac{5}{6}x - 4\)**

So the answer is:

y = \( \frac{5}{6}x - 4 \)