### Video Transcript

Determine the equation of the line
parallel to the ๐ฅ-axis that passes through negative one-half, four.

So, weโll sketch a coordinate plane
and label the ๐ฅ- and ๐ฆ-axis. Weโre given the point negative
one-half, four. Negative one-half will be halfway
between zero and negative one. And then, weโll go up four, so that
our point lies here. The line weโre looking for goes
through this point and is parallel to the ๐ฅ-axis.

Parallel lines are lines on a plane
that never intersect. Theyโre always the same distance
apart. This means the line weโre looking
for will never cross the ๐ฅ-axis. Since this point is four units away
from the ๐ฅ-axis, we know that the line will be four units away from the ๐ฅ-axis at
every point. And so, we could have a point at
one, four.

And now that we have found two
points on our line, we can sketch the line. This is the line weโre looking
for. But our job is to find its
equation. We know that this is a horizontal
line. Therefore, the slope of this line
is zero. We often write the equation of a
line in the form ๐ฆ equals ๐๐ฅ plus ๐, where ๐ is the slope and ๐ is the
๐ฆ-intercept. If we know that our slope is zero,
we have ๐ฆ equals zero ๐ฅ plus ๐, where ๐ is the ๐ฆ-intercept.

The ๐ฆ-intercept is the place where
our line crosses the ๐ฆ-axis here at four. And so, the ๐ value of our
equation would be four. Zero times ๐ฅ equals zero. That ๐ฅ term drops out and weโre
left with ๐ฆ equals four. This is because at every point
along the ๐ฅ-axis, ๐ฆ will be equal to four. The equation for this horizontal
line is ๐ฆ equals four.