Line Equation 6F2Acc

1. **State the problem:** We need to find the equation of a line with slope $m=\frac{2}{7}$ that passes through the point $(5, -6)$. 2. **Formula used:** The point-slope form of a line is $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 3. **Substitute known values:** Here, $x_1=5$, $y_1=-6$, and $m=\frac{2}{7}$. So, $$y - (-6) = \frac{2}{7}(x - 5)$$ which simplifies to $$y + 6 = \frac{2}{7}(x - 5)$$ 4. **Distribute the slope:** $$y + 6 = \frac{2}{7}x - \frac{2}{7} \times 5$$ $$y + 6 = \frac{2}{7}x - \frac{10}{7}$$ 5. **Isolate $y$:** $$y = \frac{2}{7}x - \frac{10}{7} - 6$$ 6. **Convert 6 to fraction with denominator 7:** $$6 = \frac{42}{7}$$ 7. **Combine constants:** $$y = \frac{2}{7}x - \frac{10}{7} - \frac{42}{7} = \frac{2}{7}x - \frac{52}{7}$$ **Final answer:** $$y = \frac{2}{7}x - \frac{52}{7}$$ This is the equation of the line with slope $\frac{2}{7}$ passing through $(5, -6)$.