Question

Write the equation in standard form with integer coefficients. $$y=6-5 x$$

Short answer

The equation in standard form with integer coefficients is \(5x + y = 6\).

Step-by-step solution

Identify the given equation

The given equation is \(y = 6 - 5x\).

Rearrange the equation

Rearrange the given equation to the form Ax + By = C. This involves moving terms from one side of the equation to the other to isolate y. Rearrange the equation as follows: add 5x to both sides of the equation to move it to the left side, which gives \(5x + y = 6\)

Validate the result

Check if the rearranged equation maintains the standard linear form Ax + By = C where A, B, and C are integers. In this case, A=5, B=1, and C=6, which are indeed integers.