# Video: Finding the Equation of a Straight Line Parallel to a Coordinate Axis and Passing through a Given Point

Determine the equation of the line parallel to the ๐ฅ-axis that passes through (โ1/2, 4).

02:30

### Video Transcript

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

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

Parallel lines are lines on a plane that never intersect. Theyโre always the same distance apart. This means the line weโre looking for will never cross the ๐ฅ-axis. Since this point is four units away from the ๐ฅ-axis, we know that the line will be four units away from the ๐ฅ-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 weโ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 ๐ฆ equals ๐๐ฅ plus ๐, where ๐ is the slope and ๐ is the ๐ฆ-intercept. If we know that our slope is zero, we have ๐ฆ equals zero ๐ฅ plus ๐, where ๐ is the ๐ฆ-intercept.

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