1. The problem is to understand and use the point-slope form of a linear equation. 2. The point-slope form formula is: $$y - y_1 = m(x - x_1)$$ where $m$ is the slope of the line and $(x_1, y_1)$ is a point on the line. 3. This form is useful when you know the slope of a line and one point on it, and you want to find the equation of the line. 4. For example, if the slope $m = 3$ and the point is $(2, 5)$, substitute these values into the formula: $$y - 5 = 3(x - 2)$$ 5. To simplify, distribute the slope: $$y - 5 = 3x - 6$$ 6. Then add 5 to both sides to solve for $y$: $$y = 3x - 6 + 5$$ 7. Simplify the right side: $$y = 3x - 1$$ 8. This is the slope-intercept form of the line, derived from the point-slope form. This process shows how to use the point-slope form to write the equation of a line when given a point and a slope.