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.