Question Video: Finding the Cartesian Form of the Equation of a Straight Line | Nagwa Question Video: Finding the Cartesian Form of the Equation of a Straight Line | Nagwa

Question Video: Finding the Cartesian Form of the Equation of a Straight Line Mathematics

Determine the Cartesian equation of the straight line passing through the point (−5, −5) and parallel to the 𝑦-axis.

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Video Transcript

Determine the Cartesian equation of the straight line passing through the point negative five, negative five and parallel to the 𝑦-axis.

A line that’s parallel to the 𝑦-axis is a vertical line like this one. We say that the equation of a vertical line that passes through the 𝑥-axis at some point 𝑎 is of the form 𝑥 equals 𝑎. Now, a common misconception here is to think that since it’s parallel to the 𝑦-axis, its equation is of the form 𝑦 equals some value. That’s not true. It passes through the 𝑥-axis at 𝑎. So its equation is 𝑥 equals 𝑎.

Now, one way we can establish the value of 𝑎 is to find the point at which our line passes through the 𝑥-axis. Alternatively, we know that since it’s vertical, all of its 𝑥-coordinates will be the same. We know that when 𝑥 is negative five, 𝑦 is negative five. So all of the 𝑥-coordinates on this line must be negative five. And that means the line must also pass through the 𝑥-axis and negative five.

We can therefore say that the equation of the line is 𝑥 equals negative five, although we can add five to both sides and alternatively write this as 𝑥 plus five equals zero. The equation of the straight line passing through the point negative five, negative five, which is parallel to the 𝑦-axis, is 𝑥 plus five equals zero.

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