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

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

6y=5x

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 know that parallel lines have the same slope. The slope of the given line is \( \frac{5}{6} \).

To write the equation of a line in slope-intercept form \( y = mx + b \) that has a slope of \( \frac{5}{6} \) and passes through the point \( (12, 6) \), we can use the point-slope form of the equation, which is given by:

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

Where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Plugging in the values, we have:

- \( m = \frac{5}{6} \)
- \( (x_1, y_1) = (12, 6) \)

Substituting these values into the point-slope formula:

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

Now, simplify this equation:

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

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

Calculating \( \frac{5}{6} \cdot 12 \):

\[
\frac{5 \times 12}{6} = \frac{60}{6} = 10
\]

So the equation becomes:

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

2. Add 6 to both sides:

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

This simplifies to:

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

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

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

Therefore, the correct response is:

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