Question

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

6y=5x
6 y equals 5 x

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

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

y=5/6x+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 use the fact that parallel lines have the same slope.

The slope of the given line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \). Therefore, the line we are looking for will also have a slope of \( \frac{5}{6} \).

Now, we can use the point-slope form of the equation 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.

Substituting \( m = \frac{5}{6} \), \( x_1 = 12 \), and \( y_1 = 6 \):

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

Now, let's simplify this equation:

1. Distribute \( \frac{5}{6} \):

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

2. Add 6 to both sides:

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

So the equation of the line parallel to \( y = \frac{5}{6}x \) that passes through the point (12, 6) is:

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

Thus, the correct response is:

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