Write the linear equation 𝑦 equals one-third 𝑥 plus seven in standard form.
A linear equation 𝑎𝑥 plus 𝑏𝑦 equals 𝑐, where 𝑎, 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 𝑥 plus seven so it is in the form 𝑎𝑥 plus 𝑏𝑦 equals 𝑐.
Multiplying each of our terms by three gives us three 𝑦 equals 𝑥 plus 21 as 𝑦 multiplied by three is three 𝑦, one-third 𝑥 multiplied by three is equal to 𝑥, and seven multiplied by three is equal to 21. Subtracting 𝑥 from both sides of this equation gives us negative 𝑥 plus three 𝑦 is equal to 21.
Our equation is now in standard form, where the values of 𝑎, 𝑏, and 𝑐 are negative one, three, and 21, respectively.
The linear equation 𝑦 equals one-third 𝑥 plus seven in standard form is written negative 𝑥 plus three 𝑦 equals 21.