1. **Stating the problem:** Find the slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ using the formula for slope. 2. **Formula for slope:** The slope $m$ of a line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula represents the "rise" (change in $y$) over the "run" (change in $x$). 3. **Important rules:** - If $m > 0$, the line rises from left to right. - If $m < 0$, the line falls from left to right. - If $m = 0$, the line is horizontal. - If the denominator $(x_2 - x_1) = 0$, the slope is undefined (vertical line). 4. **Example calculation:** Given points $(0,0)$ and $(2,1)$: $$m = \frac{1 - 0}{2 - 0} = \frac{1}{2}$$ So, the slope is $\frac{1}{2}$. 5. **Equation of a line using point-slope form:** Once slope $m$ is known, the equation of the line passing through $(x_1,y_1)$ is: $$y - y_1 = m(x - x_1)$$ 6. **Slope-intercept form:** Rearranging the above gives: $$y = mx + b$$ where $b$ is the y-intercept. 7. **Summary:** - Use $m = \frac{y_2 - y_1}{x_2 - x_1}$ to find slope. - Use $y - y_1 = m(x - x_1)$ for line equation. - Convert to $y = mx + b$ for slope-intercept form. This completes the explanation of slope and line equations.