Find the coordinates of the point where 𝑥 over two plus 𝑦 over three equals one intersects the 𝑦-axis.
We begin by noticing that our equation is written in two-intercept form. This can be defined as follows. The two-intercept form of the equation of the straight line that intercepts the 𝑥-axis at 𝑎, zero and intercepts the 𝑦-axis at zero, 𝑏 is 𝑥 over 𝑎 plus 𝑦 over 𝑏 equals one. This can be represented on the 𝑥𝑦-coordinate plane as shown.
In this question, 𝑎 is equal to two and 𝑏 is equal to three. We are interested in the point at which the graph intersects the 𝑦-axis. As this occurs at zero, 𝑏, we can conclude that the coordinates of the point where 𝑥 over two plus 𝑦 over three equals one intersects the 𝑦-axis is zero, three.