# Video: Finding the π¦-Intercept of a Linear Function

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

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### Video Transcript

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

The π¦-intercept is the place where the function crosses the π¦-axis. Another way to say that, is the coordinate of π¦ when π₯ is zero. And when a function is written as π¦ equals ππ₯ plus π, the π represents the π¦-intercept.

Our function is written as three π¦ equals 15π₯ plus 18. How can we change our function to be in the format π¦ equals ππ₯ plus π? Hereβs the difference. In π¦ equals ππ₯ plus π, the π¦ is isolated. Thereβs nothing being multiplied by the π¦. So letβs isolate our π¦.

Right now, our π¦ is being multiplied by three. To isolate π¦, weβll divide by three on both sides of the equation. Three times π¦ divided by three, and then 15π₯ plus 18 divided by three. On the left side, our threes cancel out leaving us with π¦. 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, π¦ equals ππ₯ plus π, whatever values in the π position is our π¦-intercept. For this function, the π¦-intercept equals six.

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