Question

Which line of parallel to line y equals 5/6x and go through the points 12, 6

Answer 1

To find a line that is parallel to the given 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 is \(\frac{5}{6}\).

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

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

Where \(m\) is the slope, and \((x_1, y_1)\) is the point the line goes through. In this case, \(m = \frac{5}{6}\) and \((x_1, y_1) = (12, 6)\).

Substituting these values into the point-slope equation:

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

Now, distribute the slope on the right side:

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

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

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

So we now have:

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

Next, 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:

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