1. **State the problem:** Solve the linear equation $3x + 7y = 21$ for $y$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving other terms to the opposite side and then dividing by the coefficient of $y$. 3. **Isolate $y$:** $$3x + 7y = 21$$ Subtract $3x$ from both sides: $$7y = 21 - 3x$$ 4. **Divide both sides by 7:** $$y = \frac{21 - 3x}{7}$$ Show canceling common factors: $$y = \frac{\cancel{21} - 3x}{\cancel{7}}$$ Since 21 and 7 share a factor of 7, simplify: $$y = 3 - \frac{3}{7}x$$ 5. **Final answer:** $$y = 3 - \frac{3}{7}x$$ This means for any value of $x$, you can find $y$ using this formula. The graph of this equation is a straight line with slope $-\frac{3}{7}$ and $y$-intercept 3.