Video: Finding the 𝑦-Intercept of a Linear Function

What is the 𝑦-intercept of the function 3𝑦 = 15π‘₯ + 18?

01:54

Video Transcript

What is the 𝑦-intercept of the function three 𝑦 equals 15π‘₯ plus eight [18]?

The 𝑦-intercept is the place where the function crosses the 𝑦-axis. Another way to say that, is the coordinate of 𝑦 when π‘₯ is zero. And when a function is written as 𝑦 equals π‘šπ‘₯ plus 𝑏, the 𝑏 represents the 𝑦-intercept.

Our function is written as three 𝑦 equals 15π‘₯ plus 18. How can we change our function to be in the format 𝑦 equals π‘šπ‘₯ plus 𝑏? Here’s the difference. In 𝑦 equals π‘šπ‘₯ 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 15π‘₯ 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 15π‘₯ divided by three plus 18 divided by three. 15π‘₯ divided by three equals five π‘₯. 18 divided by three equals six.

Once our function is in this form, 𝑦 equals π‘šπ‘₯ plus 𝑏, whatever values in the 𝑏 position is our 𝑦-intercept. For this function, the 𝑦-intercept equals six.

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