1. The problem is to find the y-intercept $b$ in the linear equation $y = mx + b$ given a point and the slope. 2. The formula for a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. You are given the slope $m = 3$ and a point $(5,5)$ on the line. 4. Substitute the slope and the coordinates of the point into the equation: $$5 = 3(5) + b$$ Here, the first 5 is the $y$-value of the point, and the second 5 inside the parentheses is the $x$-value. 5. Simplify the right side: $$5 = 15 + b$$ 6. Solve for $b$ by subtracting 15 from both sides: $$5 - \cancel{15} = \cancel{15} + b - 15$$ $$-10 = b$$ 7. So, the y-intercept is $b = -10$. 8. The equation of the line is therefore: $$y = 3x - 10$$ In summary, the first 5 is the $y$-coordinate of the point, and the second 5 is the $x$-coordinate. You substitute $x$ and $y$ values from the point into the equation to solve for $b$.