1. The problem is to find the y-intercept $b$ of the line given the slope $m=3$ and a point on the line. 2. The equation of a line in slope-intercept form is: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. To find $b$, we substitute the slope $m=3$ and the coordinates of a known point on the line into the equation. The point used here is $(5,5)$, meaning $x=5$ and $y=5$. 4. Substitute these values: $$5 = 3(5) + b$$ 5. Simplify the right side: $$5 = 15 + b$$ 6. To isolate $b$, subtract 15 from both sides: $$5 - 15 = b$$ $$\cancel{5} - 15 = b$$ 7. Calculate the left side: $$-10 = b$$ 8. Therefore, the y-intercept is $b = -10$, and the equation of the line is: $$y = 3x - 10$$ **Answer:** The 5 came from the $y$-coordinate of the point $(5,5)$ used to find $b$.