1. The problem is to find the equation of a line passing through two points or to analyze a coordinate geometry problem. 2. The general formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$m=\frac{y_2-y_1}{x_2-x_1}$$ 3. Once the slope is found, the equation of the line can be written using point-slope form: $$y-y_1=m(x-x_1)$$ 4. Important rules: - The slope formula calculates the steepness of the line. - If $x_2=x_1$, the line is vertical and the slope is undefined. - Simplify fractions by canceling common factors. 5. Example intermediate work for slope calculation: $$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-2}{4-1}=\frac{4}{3}$$ 6. Writing the line equation using point $(1,2)$: $$y-2=\frac{4}{3}(x-1)$$ 7. Simplify the equation: $$y-2=\frac{4}{3}x-\frac{4}{3}$$ $$y=\frac{4}{3}x-\frac{4}{3}+2$$ $$y=\frac{4}{3}x-\frac{4}{3}+\frac{6}{3}$$ $$y=\frac{4}{3}x+\frac{2}{3}$$ This is the equation of the line in slope-intercept form.