Question

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

Answer 1

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

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

Substituting \( m = \frac{5}{6} \) and the point \( (12, 6) \):

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

Now, to put this in slope-intercept form (\( y = mx + b \)), we will distribute and solve for \( y \):

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

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

Calculating \( -\frac{5}{6} \times 12 \):

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

2. Therefore, the equation becomes:

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

3. Now, add 6 to both sides:

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

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

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