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 (โˆ’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‘š๐‘ฅ plus ๐‘, where ๐‘š 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.

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