Video Transcript
At which point do the lines 𝑥
equals seven and one-sixth 𝑦 equals negative one intersect?
In this question, we have the
equations of two lines and we’re asked where these two lines intersect, which would
be the point where they meet or cross. It might be useful to begin by
visualizing what these two lines would look like on the coordinate plane. The line 𝑥 equals seven indicates
all the ordered pairs that have an 𝑥-value of seven. And so we’ll have a vertical line
that goes through seven on the 𝑥-axis.
For the second equation of
one-sixth 𝑦 equals negative one, sometimes it’s easier to visualize the equation of
a line like this if we write the equation with 𝑦 as the subject. Rearranging by multiplying through
by six would give us the equation of 𝑦 equals negative six. So, the equation of the line 𝑦
equals negative six, or one-sixth 𝑦 equals negative one, will be a horizontal line
passing through negative six on the 𝑦-axis.
The intersection point then is the
ordered pair where these two lines intersect. Using the graph, we can see that
this occurs at the point seven, negative six. And so this is the answer for the
intersection point of the two lines.
If we wanted to consider an
algebraic method here instead of drawing the lines, usually when we find the
intersection of two lines, we could set the equations equal to each other. But as we had a horizontal line and
a vertical line here, the only point where these two have the same 𝑥- and 𝑦-values
is when 𝑥 is equal to seven and 𝑦 is equal to negative six, which would also give
us the coordinates seven, negative six.
