# 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 𝑥-axis that passes through (−1/2, 4).

02:30

### Video Transcript

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 one, four.

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.