Video: Finding the π‘₯ and 𝑦 Intercepts of a Line

What are the π‘₯-intercept and 𝑦-intercept of the line 3π‘₯ + 2𝑦 βˆ’ 12 = 0?

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Video Transcript

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

The π‘₯-intercept is where the graph of a line crosses the π‘₯-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 π‘₯-intercept will be some π‘₯-value and then zero. And the coordinate for the 𝑦-intercept will be zero, followed by some 𝑦-value.

For the line three π‘₯ plus two 𝑦 minus 12 equals zero, to find the π‘₯-intercept, we plug in a value of zero for 𝑦 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.

We’ll follow the same procedure to find the 𝑦-intercept. However, in this case we’ll be plugging in a zero for the π‘₯-value. When π‘₯ 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 π‘₯-intercept by substituting 𝑦 equals zero into our equation and the 𝑦-intercept by substituting π‘₯ equals zero into our equation.

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