### Video Transcript

Write the linear equation π¦ equals one-third π₯ plus seven in standard form.

A linear equation ππ₯ plus ππ¦ equals π, where π, π, and π are integers, is said to be in standard form. In this example, we need to rearrange the equation π¦ equals one-third π₯ plus seven so it is in the form ππ₯ plus ππ¦ equals π.

Multiplying each of our terms by three gives us three π¦ equals π₯ plus 21 as π¦ multiplied by three is three π¦, one-third π₯ multiplied by three is equal to π₯, and seven multiplied by three is equal to 21. Subtracting π₯ from both sides of this equation gives us negative π₯ plus three π¦ is equal to 21.

Our equation is now in standard form, where the values of π, π, and π are negative one, three, and 21, respectively.

The linear equation π¦ equals one-third π₯ plus seven in standard form is written negative π₯ plus three π¦ equals 21.