Question

Which line is parallel to the line y=5/6x 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

Answer 1

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

The slope of the line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \). Therefore, the equation of the line that is parallel to it and goes through the point \( (12, 6) \) can be found using the point-slope form of a linear equation:

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

Where:
- \( m \) is the slope,
- \( (x_1, y_1) \) is the point through which the line passes.

Substituting in the values:

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

Now, let's simplify this equation:

1. Distribute the slope on the right side:
\[
y - 6 = \frac{5}{6}x - \frac{5}{6} \times 12
\]
\[
y - 6 = \frac{5}{6}x - 10
\]

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 \( y = \frac{5}{6}x \) and passing through the point \( (12, 6) \) is:

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

Among the given responses, the correct one is:

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