Answer
Point-slope: $y+7 = -2(x - 4)$
General form: $y = -2x + 1$
Work Step by Step
$$x - 2y - 3 = 0$$ $$x - 3 = 2y$$ $$\frac{1}{2}x - \frac{3}{2} = y$$ where the slope $m = \frac{1}{2}$ and the y-intercept $b = -\frac{3}{2}$. To find a perpendicular line, we need a slope $m_{perpendicular}$ that, when multiplied by the original slope, results in $-1$. In this case, $$\frac{1}{2}m_{perpendicular} = -1$$ $$m_{perpendicular} = -2$$. Since we have the point of intersection between both lines $(4, -7)$, we can now write the equation for the perpendicular line as follows: $$y-(-7) = -2(x - 4)$$ $$y + 7 = -2(x - 4)$$ which is in slope-point form, and $$y = -2x + 8 - 7$$ $$y = 2x +1$$ which is in general form.
