For every value of k, the line y = k(x-3) + 5 passes through the same fixed point, regardless of the value of k. What is the y-coordinate…

The line is written as $y = k(x - 3) + 5$. If $x = 3$, the term $k(x-3)$ becomes $k \cdot 0 = 0$ no matter what $k$ is, leaving $y = 5$. So every line in the family passes through the point $(3, 5)$, and the $y$-coordinate is 5. This is point-slope form, $y - y_1 = m(x - x_1)$, with $m = k$, $x_1 = 3$ and $y_1 = 5$, so the fixed point can be read straight from the equation. A common wrong answer is $-3$, which comes from taking the number inside the parentheses, and another is 2, from computing $5 - 3$.