Video: Writing Linear Equations in Standard Form

Write the linear equation 𝑦 = (1/3)π‘₯ + 7 in standard form.

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Video Transcript

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

A linear equation π‘Žπ‘₯ plus 𝑏𝑦 equals 𝑐, where π‘Ž, 𝑏, and 𝑐 are integers, is said to be in standard form. In this example, we need to rearrange the equation 𝑦 equals one-third π‘₯ plus seven so it is in the form π‘Žπ‘₯ plus 𝑏𝑦 equals 𝑐.

Multiplying each of our terms by three gives us three 𝑦 equals π‘₯ plus 21 as 𝑦 multiplied by three is three 𝑦, 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 𝑦 is equal to 21.

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

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

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