Question Video: Finding the π‘₯-Intercept and the 𝑦-Intercept Mathematics

The graph of the equation (π‘₯/4) + (𝑦/12) = 1 is a straight line. What are the coordinates of the π‘₯-intercept of the line? What are the coordinates of the 𝑦-intercept of the line? What is the slope of the line?

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Video Transcript

The graph of the equation π‘₯ over four plus 𝑦 over 12 equals one is a straight line. What are the coordinates of the π‘₯-intercept of the line? What are the coordinates of the 𝑦-intercept of the line? What is the slope of the line?

We should notice that the equation we’ve been given is in the two-intercept form of the equation of a straight line, π‘₯ over π‘Ž plus 𝑦 over 𝑏 equals one. And we know that for a line given in this form, the coordinates of its π‘₯-intercept are π‘Ž, zero and the coordinates of its 𝑦-intercept are zero, 𝑏. We can therefore determine the coordinates of the π‘₯- and 𝑦-intercepts of this line by comparing the equation we’ve been given with the general form and determining the values of π‘Ž and 𝑏, which are the denominators of the two quotients. We see first that the value of π‘Ž, that’s the value by which π‘₯ is divided, is four, and so the coordinates of the π‘₯-intercept are four, zero. In the same way, the value of 𝑏 is 12, and so the coordinates of the 𝑦-intercept are zero, 12.

Next, we consider the slope of this line. Now, we could calculate it using the coordinates of the two points we’ve determined to lie on the line. Or we could recall a general result, which is that the slope of a straight line whose equation is given in the two-intercept form is equal to negative 𝑏 over π‘Ž. Our value of 𝑏 we’ve just determined to be 12 and the value of π‘Ž is four. So we have π‘š equals negative 12 over four, which is equal to negative three. So we’ve completed the question. The coordinates of the π‘₯-intercept are four, zero; the coordinates of the 𝑦-intercept are zero, 12; and the slope of this line is negative three.

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