What is the 𝑦-intercept of the function three 𝑦 equals 15𝑥 plus
The 𝑦-intercept is the place where the function crosses the 𝑦-axis. Another way to say that, is the coordinate of 𝑦 when 𝑥 is zero. And when a function is written as 𝑦 equals 𝑚𝑥 plus 𝑏, the 𝑏 represents the 𝑦-intercept.
Our function is written as three 𝑦 equals 15𝑥 plus 18. How can we change our function to be in the format 𝑦 equals 𝑚𝑥 plus 𝑏? Here’s the difference. In 𝑦 equals 𝑚𝑥 plus 𝑏, the 𝑦 is isolated. There’s nothing being multiplied by the 𝑦. So let’s isolate our 𝑦.
Right now, our 𝑦 is being multiplied by three. To isolate 𝑦, we’ll divide by three on both sides of the equation. Three times 𝑦 divided by three, and then 15𝑥 plus 18 divided by three. On the left side, our threes cancel out leaving us with 𝑦. On our right side, we need to divide each term by three, which means 15𝑥 divided by three plus 18 divided by three. 15𝑥 divided by three equals five 𝑥. 18 divided by three equals six.
Once our function is in this form, 𝑦 equals 𝑚𝑥 plus 𝑏, whatever values in the 𝑏 position is our 𝑦-intercept. For this function, the 𝑦-intercept equals six.