Video Transcript
The graph of the equation 𝑥 over
four plus 𝑦 over 12 equals one is a straight line. What are the coordinates of the
𝑥-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, 𝑥
over 𝑎 plus 𝑦 over 𝑏 equals one. And we know that for a line given
in this form, the coordinates of its 𝑥-intercept are 𝑎, zero and the coordinates
of its 𝑦-intercept are zero, 𝑏. We can therefore determine the
coordinates of the 𝑥- and 𝑦-intercepts of this line by comparing the equation
we’ve been given with the general form and determining the values of 𝑎 and 𝑏,
which are the denominators of the two quotients. We see first that the value of 𝑎,
that’s the value by which 𝑥 is divided, is four, and so the coordinates of the
𝑥-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 𝑎. Our value of 𝑏 we’ve just
determined to be 12 and the value of 𝑎 is four. So we have 𝑚 equals negative 12
over four, which is equal to negative three. So we’ve completed the
question. The coordinates of the 𝑥-intercept
are four, zero; the coordinates of the 𝑦-intercept are zero, 12; and the slope of
this line is negative three.
