Question Video: Finding the 𝑥- and 𝑦-Intercepts of a Line Mathematics

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.