# Question Video: Finding the π₯-Intercept and the π¦-Intercept Mathematics

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

We should notice that the equation weβve been given is in the two-intercept form of the equation of a straight line, π₯ over π plus π¦ over π equals one. And we know that for a line given in this form, the coordinates of its π₯-intercept are π, zero and the coordinates of its π¦-intercept are zero, π. We can therefore determine the coordinates of the π₯- and π¦-intercepts of this line by comparing the equation weβve been given with the general form and determining the values of π and π, which are the denominators of the two quotients. We see first that the value of π, thatβ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 π is 12, and so the coordinates of the π¦-intercept are zero, 12.

Next, we consider the slope of this line. Now, we could calculate it using the coordinates of the two points weβ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 π over π. Our value of π weβve just determined to be 12 and the value of π is four. So we have π equals negative 12 over four, which is equal to negative three. So weβve completed the question. The coordinates of the π₯-intercept are four, zero; the coordinates of the π¦-intercept are zero, 12; and the slope of this line is negative three.