1. **State the problem:** Solve the linear equation $7x - 5y = 26$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. This involves moving terms and dividing by the coefficient of $y$. 3. **Isolate $y$:** $$7x - 5y = 26$$ Subtract $7x$ from both sides: $$-5y = 26 - 7x$$ 4. **Divide both sides by $-5$ to solve for $y$:** $$y = \frac{26 - 7x}{-5}$$ Show cancellation of the negative sign: $$y = \frac{\cancel{26 - 7x}}{\cancel{-5}} = -\frac{26 - 7x}{5}$$ 5. **Simplify the expression:** $$y = -\frac{26}{5} + \frac{7x}{5}$$ 6. **Final answer:** $$y = \frac{7}{5}x - \frac{26}{5}$$ This expresses $y$ as a function of $x$ in slope-intercept form, where the slope is $\frac{7}{5}$ and the $y$-intercept is $-\frac{26}{5}$.