The equation 5x + by = 20 has a y-intercept of 4. What is the value of b?

The $y$-intercept is the point where $x = 0$, and here it is $(0, 4)$. Substitute into $5x + by = 20$: $5(0) + b(4) = 20$, so $4b = 20$ and $b = 5$. Check: with $b = 5$, the equation $5x + 5y = 20$ gives $y = 4$ at $x = 0$. A common wrong answer is 4, which is the intercept itself, not the coefficient. Another is 20, the constant on the right, and a third is $\frac{1}{5}$ from inverting the division. Substitute the point, then solve for the unknown coefficient.