Question Video: Finding the 𝑥-Intercept and the 𝑦-Intercept Mathematics

Video Transcript

List the coordinates of the 𝑥-intercept and the 𝑦-intercept of the line 𝑥 over three minus 𝑦 over two is equal to one.

Now, looking carefully at the form in which the equation of this line has been given, we should notice that it looks very similar to the two-intercept form of the equation of a straight line. The two-intercept form is 𝑥 over 𝑎 plus 𝑦 over 𝑏 equals one, where the line intercepts the 𝑥-axis at 𝑎, zero and intercepts the 𝑦-axis at zero, 𝑏. However, if we look really closely at this equation, we see that there is a subtraction sign rather than an addition sign between the two terms on the left-hand side. We therefore need to manipulate the equation we’ve been given so that it matches up fully with the two-intercept form. And we’ll then be able to use it to determine the coordinates of the 𝑥- and 𝑦-intercepts.

From our knowledge of algebra, we know that subtracting 𝑦 over two is the same as adding negative 𝑦 over two or we can think of this as adding 𝑦 over negative two. It doesn’t matter whether we write that negative in the numerator or denominator of the quotient. So we can take this equation 𝑥 over three minus 𝑦 over two equals one and rewrite it as 𝑥 over three plus 𝑦 over negative two equals one. The only change is in that second term. Now we wouldn’t usually choose to leave a negative value in the denominator of a quotient like this. But by doing this, our equation now matches up exactly with the format of the two-intercept form of the equation of a straight line.

We can therefore determine the 𝑥- and 𝑦-intercepts by considering the denominators of the two quotients. The denominator for the 𝑥-term is three, which tells us that the value of 𝑎 is three, and so the coordinates of the 𝑥-intercept are three, zero. Looking at the second term, we see that the denominator for 𝑦 is negative two. This tells us then that the value of 𝑏 is negative two, and so the coordinates of the 𝑦-intercept are zero, negative two. By manipulating the equation we were given slightly so that it perfectly matches up with the two-intercept form of the equation of a straight line, we found that the coordinates of the 𝑥-intercept of this line are three, zero and the coordinates of the 𝑦-intercept are zero, negative two.