### Video Transcript

What are the 𝑥-intercept and
𝑦-intercept of the line three 𝑥 plus two 𝑦 minus 12 equals zero?

We begin by recalling that the
𝑥-intercept is the point at which our graph crosses the 𝑥-axis. And this means that the
𝑦-coordinate must be equal to zero. Likewise, the 𝑦-intercept is the
point at which the graph crosses the 𝑦-axis. And at this point, the
𝑥-coordinate equals zero. This can be represented on the
𝑥𝑦-coordinate plane as shown. The 𝑥-intercept has coordinates
𝑎, zero and the 𝑦-intercept coordinates zero, 𝑏. It is these values of 𝑎 and 𝑏
that we are trying to calculate in this question.

Substituting 𝑥 equals 𝑎 and 𝑦
equals zero into our equation, we have three multiplied by 𝑎 plus two multiplied by
zero minus 12 equals zero. The left-hand side simplifies to
three 𝑎 minus 12. We can then add 12 to both sides
such that three 𝑎 is equal to 12. And dividing through by three gives
us 𝑎 is equal to four. The point at which the line
intersects the 𝑥-axis is four, zero. And as such, the 𝑥-intercept is
four.

Substituting 𝑥 equals zero and 𝑦
equals 𝑏 into our equation, we have three multiplied by zero plus two multiplied by
𝑏 minus 12 equals zero. This simplifies to two 𝑏 minus 12
equals zero. Adding 12 to both sides and then
dividing through by two, we have 𝑏 is equal to six. The graph passes through the
𝑦-axis at the point zero, six. And we can therefore conclude that
the 𝑦-intercept is six. The 𝑥- and 𝑦-intercepts of the
line three 𝑥 plus two 𝑦 minus 12 equals zero are four and six, respectively.