1. We are given two points: $(5,2)$ and $(-2,-12)$. 2. The goal is to find the equation of the line passing through these points in standard form and general form. 3. First, calculate the slope $m$ using the formula: $$m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{-12 - 2}{-2 - 5} = \frac{-14}{-7} = 2$$ 4. Use point-slope form with point $(5,2)$: $$y - y_1 = m(x - x_1)$$ $$y - 2 = 2(x - 5)$$ 5. Simplify: $$y - 2 = 2x - 10$$ $$y = 2x - 8$$ 6. To write in standard form $Ax + By = C$, rearrange: $$y = 2x - 8$$ $$-2x + y = -8$$ 7. Multiply both sides by $-1$ to make $A$ positive: $$\cancel{-1}(-2x + y) = \cancel{-1}(-8)$$ $$2x - y = 8$$ 8. The general form is the same as standard form here: $$2x - y - 8 = 0$$ Final answers: - Standard form: $2x - y = 8$ - General form: $2x - y - 8 = 0$