Video Transcript
The straight lines eight 𝑥 plus
five 𝑦 equals eight and eight 𝑥 plus 𝑎𝑦 equals negative eight are parallel. What is the value of 𝑎?
We know that parallel lines have
the same slope. And in slope–intercept form, 𝑦
equals 𝑚𝑥 plus 𝑏, the coefficient of the 𝑥-variable 𝑚 represents the slope. We’ve been told that these two
lines are parallel. And that means they will have the
same slope. To find the slope of these lines,
we’ll convert them to slope–intercept form. To do that, we get 𝑦 by
itself. Since both equations have eight 𝑥
on the left, we’ll subtract eight 𝑥 from both sides of both equations. On the left, we would have five 𝑦
equals negative eight 𝑥 plus eight. And on the right, 𝑎𝑦 equals
negative eight 𝑥 minus eight. We need to get 𝑦 by itself for
slope–intercept form. So, we can divide through by
five. And the equation on the left in
slope–intercept form will be 𝑦 equals negative eight-fifths 𝑥 plus
eight-fifths.
On the right, we need to do
something similar. To get 𝑦 by itself, we’ll divide
through by 𝑎. And our second equation will be 𝑦
equals negative eight over 𝑎𝑥 minus eight over 𝑎. These slopes have to be equal to
each other if these lines are parallel. Since one of the slopes is negative
eight over five, the other slope will need to be negative eight over five. And that tells us that 𝑎 must be
five for these two lines to be parallel. If we go back in and plug in five
for 𝑎, we see that the ratio of coefficients between these two equations are equal
to each other, which makes them parallel.
