Question

1. write in standard form with integer coefficients

$y = \frac{1}{8}x + \frac{3}{8}$

Explanation:

Step1: Recall standard form

The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\geq0\). We start with the given equation \(y=\frac{1}{8}x+\frac{3}{8}\).

Step2: Eliminate fractions

Multiply every term in the equation by 8 to get rid of the denominators.
\(8\times y = 8\times(\frac{1}{8}x+\frac{3}{8})\)
\(8y=x + 3\)

Step3: Rearrange into standard form

Subtract \(x\) from both sides to get \( -x+8y = 3\). We can also multiply through by - 1 to make the coefficient of \(x\) positive (since \(A\geq0\) in standard form), so \(x - 8y=-3\).

Answer:

The standard form with integer coefficients is \(x - 8y=-3\) (or \(-x + 8y = 3\) is also correct but usually we prefer \(A\geq0\) so \(x - 8y=-3\) is more standard).