Determine the equation of the line
parallel to the 𝑥-axis that passes through negative one-half, four.
So, we’ll sketch a coordinate plane
and label the 𝑥- and 𝑦-axis. We’re given the point negative
one-half, four. Negative one-half will be halfway
between zero and negative one. And then, we’ll go up four, so that
our point lies here. The line we’re looking for goes
through this point and is parallel to the 𝑥-axis.
Parallel lines are lines on a plane
that never intersect. They’re always the same distance
apart. This means the line we’re looking
for will never cross the 𝑥-axis. Since this point is four units away
from the 𝑥-axis, we know that the line will be four units away from the 𝑥-axis at
every point. And so, we could have a point at
And now that we have found two
points on our line, we can sketch the line. This is the line we’re 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 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is the slope and 𝑏 is the
𝑦-intercept. If we know that our slope is zero,
we have 𝑦 equals zero 𝑥 plus 𝑏, where 𝑏 is the 𝑦-intercept.
The 𝑦-intercept is the place where
our line crosses the 𝑦-axis here at four. And so, the 𝑏 value of our
equation would be four. Zero times 𝑥 equals zero. That 𝑥 term drops out and we’re
left with 𝑦 equals four. This is because at every point
along the 𝑥-axis, 𝑦 will be equal to four. The equation for this horizontal
line is 𝑦 equals four.