What are the 𝑥-intercept and 𝑦-intercept of the line three 𝑥 plus two 𝑦 minus 12 equals zero?
The 𝑥-intercept is where the graph of a line crosses the 𝑥-axis, and the 𝑦-intercept is where the graph of a line crosses the 𝑦-axis. If we think about our coordinate grid and we include the graph of a line, the coordinate for the 𝑥-intercept will be some 𝑥-value and then zero. And the coordinate for the 𝑦-intercept will be zero, followed by some 𝑦-value.
For the line three 𝑥 plus two 𝑦 minus 12 equals zero, to find the 𝑥-intercept, we plug in a value of zero for 𝑦 and then solve for 𝑥. When we do that, we get three 𝑥 minus 12 equals zero. Then we add 12 to both sides and divide through by three to find 𝑥 equals four. This means the 𝑥-intercept is located at the coordinate four, zero.
We’ll follow the same procedure to find the 𝑦-intercept. However, in this case we’ll be plugging in a zero for the 𝑥-value. When 𝑥 equals zero, we find the 𝑦-intercept. We end up with two 𝑦 minus 12 equals zero. We add 12 to both sides and then divide through by two to find that 𝑦 equals six. We therefore can say that the 𝑦-intercept is located at the point zero, six.
We were able to find the 𝑥-intercept by substituting 𝑦 equals zero into our equation and the 𝑦-intercept by substituting 𝑥 equals zero into our equation.