Video: Writing Linear Equations in Standard Form

Write the linear equation 3𝑦 = 5 − 4𝑥 in standard form.

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Video Transcript

Write the linear equation three 𝑦 equals five minus four 𝑥 in standard form.

So we were to take this linear equation and write it in standard form. And standard form is 𝐴𝑥 plus 𝐵𝑦 equals 𝐶, where 𝐴 and 𝐵 are integers and 𝐶 is a constant — meaning a number without a variable next to it. So we have three 𝑦 equals five minus four 𝑥. So the five is the constant. It’s the only one that does have a variable with it.

So let’s go ahead and move the four 𝑥 over to the left-hand side of the equation. And we’ll do so by adding four 𝑥 to both sides of the equation. They cancel on the right-hand side, but on the left four 𝑥 and three 𝑦 cannot be combined. They’re different variables. So we have a four 𝑥 plus three 𝑦 equals five.

So four would be 𝐴, three would be 𝐵, and five would be 𝐶. 𝐴 should be next to 𝑥, 𝐵 should be next to 𝑦, and 𝐶 is all by itself.

So our linear equation written in standard form is four 𝑥 plus three 𝑦 equals five.

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