1. The problem is to express $y$ in terms of $x$ from the linear equation $ax + by = k$. 2. The formula used is to isolate $y$ on one side of the equation. We start with: $$ax + by = k$$ 3. Subtract $ax$ from both sides: $$\cancel{ax} + by = k - \cancel{ax} \implies by = k - ax$$ 4. Divide both sides by $b$ to solve for $y$: $$y = \frac{k - ax}{b}$$ 5. This is the expression for $y$ in terms of $x$. It shows that $y$ depends linearly on $x$ with slope $-\frac{a}{b}$ and intercept $\frac{k}{b}$. 6. Important rules: - $b$ must not be zero to divide by it. - This form is useful for graphing or analyzing the line. Final answer: $$y = \frac{k - ax}{b}$$