### Video Transcript

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

The π₯-intercept is where the graph of a line crosses the π₯-axis, and the π¦-intercept is where the graph of a line crosses the π¦-axis. If we think about our coordinate grid and we include the graph of a line, the coordinate for the π₯-intercept will be some π₯-value and then zero. And the coordinate for the π¦-intercept will be zero, followed by some π¦-value.

For the line three π₯ plus two π¦ minus 12 equals zero, to find the π₯-intercept, we plug in a value of zero for π¦ and then solve for π₯. When we do that, we get three π₯ minus 12 equals zero. Then we add 12 to both sides and divide through by three to find π₯ equals four. This means the π₯-intercept is located at the coordinate four, zero.

Weβll follow the same procedure to find the π¦-intercept. However, in this case weβll be plugging in a zero for the π₯-value. When π₯ equals zero, we find the π¦-intercept. We end up with two π¦ minus 12 equals zero. We add 12 to both sides and then divide through by two to find that π¦ equals six. We therefore can say that the π¦-intercept is located at the point zero, six.

We were able to find the π₯-intercept by substituting π¦ equals zero into our equation and the π¦-intercept by substituting π₯ equals zero into our equation.