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

6y=5x
6 y equals 5 x

y=5/6x−4

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, any line parallel to it will also have a slope of \( \frac{5}{6} \).

Next, we can use the point-slope form of the equation of a line, which is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through.

Substituting in our values, we have:
- \( m = \frac{5}{6} \)
- \( (x_1, y_1) = (12, 6) \)

Using the point-slope formula:

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

Now, we can simplify this to slope-intercept form \( y = mx + b \):

\[
y - 6 = \frac{5}{6}x - \frac{5}{6} \cdot 12
\]
\[
y - 6 = \frac{5}{6}x - 10
\]
\[
y = \frac{5}{6}x - 10 + 6
\]
\[
y = \frac{5}{6}x - 4
\]

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

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

Thus, the correct choice from the responses is:

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