Video Transcript
Find the equations of the lines
parallel to the two axes that pass through negative two, negative 10.
Let’s sketch this out. Here is our point negative two,
negative 10. There are a pair of lines that pass
through this point which are parallel to the two axes. So we have one horizontal line and
one vertical line. Remember, the equation of a
horizontal line that passes through the 𝑦-axis at some value 𝑎 is of the form 𝑦
equals 𝑎. Whereas a vertical line that passes
through the 𝑥-axis at some point 𝑏 has the equation 𝑥 equals 𝑏.
Our job is to find the values of 𝑎
and 𝑏. Let’s begin with our horizontal
line. We know that on the horizontal
line, all 𝑦-coordinates remain unchanged. Well, according to our point, when
𝑥 is negative two, 𝑦 is negative 10. So the 𝑦-coordinate will always be
negative 10 on this horizontal line. It must, therefore, pass through
the 𝑦-axis at negative 10. And so we can say its equation is
𝑦 equals negative 10.
Similarly, we know that for
vertical lines, their 𝑥-coordinates remain unchanged. Now, according to our point, when
𝑥 is negative two, 𝑦 is negative 10. So the 𝑥-coordinates on our
vertical line will always be negative two. And so the equation of our vertical
line is 𝑥 equals negative two. The equations of the lines parallel
to the two axes that pass through negative two, negative 10 are 𝑥 equals negative
two and 𝑦 equals negative 10.
