# Question Video: Finding the π₯- and π¦-Intercepts of a Line Mathematics • 9th Grade

What are the π₯-intercept and π¦-intercept of the line 3π₯ + 2π¦ β 12 = 0?

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### Video Transcript

What are the π₯-intercept and π¦-intercept of the line three π₯ plus two π¦ minus 12 equals zero?

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

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

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