Question

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

Answer 1

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

The slope of the line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \).

Now, we can use the point-slope form of a line's equation, which is:

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

where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Here, we have \( m = \frac{5}{6} \) and the point \( (12, 6) \).

Substituting in these values, we get:

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

Now we distribute the slope:

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

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

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

Now, substituting that back into the equation gives:

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

Adding 6 to both sides:

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

This simplifies to:

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

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

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