Question

Which line is parallel to the line y=5/6x 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 that goes through the point (12, 6), we first note that parallel lines have the same slope.

The slope of the given line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \). Therefore, the line we want 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 the point through which the line passes.

Here, \( m = \frac{5}{6} \) and the point is \( (12, 6) \). Plugging in these values, we have:
\[
y - 6 = \frac{5}{6}(x - 12)
\]

Now, simplifying this equation:
\[
y - 6 = \frac{5}{6}x - \frac{5}{6} \cdot 12
\]
\[
y - 6 = \frac{5}{6}x - 10
\]
\[
y = \frac{5}{6}x - 10 + 6
\]
\[
y = \frac{5}{6}x - 4
\]

Thus, the equation of the line that is parallel to \( y = \frac{5}{6}x \) and passes through the point \( (12, 6) \) is:
\[
y = \frac{5}{6}x - 4
\]