Question

consider the line 4x+9y=-8find the equation of the line that is perpendicular to this line and passes through the point (-2, -2)find the equation of the line that is parallel of this line and passes through the point (-2, -2)

Answer 1

$\begin{gathered} \text{The equation of the line is,} \\ 4x+9y=-8 \\ 9y=-4x-8 \\ y=-\frac{4}{9}x-\frac{8}{9} \\ \text{The slope is}\Rightarrow m=-\frac{4}{9} \\ perpendicular\text{ slope}\Rightarrow m^{\prime}=\frac{9}{4} \\ 1. \\ x_1=-2,y_1=-2 \\ So,\text{ the perpendicular equation of line is} \\ y-y_1=m^{\prime}(x-x_1) \\ y+2=\frac{9}{4}(x+2) \\ 4y+8=9x+18 \\ 4y=9x+10 \\ y=\frac{9}{4}x+\frac{5}{2}(\text{Ans)} \\ 2. \\ The\text{ parallel equation is,} \\ y-y_1=m(x-x_1) \\ y+2=-\frac{4}{9}(x+2) \\ 9y+18=-4x-8 \\ 9y=-4x-26 \\ y=-\frac{4}{9}x-\frac{26}{9}(\text{Ans)} \end{gathered}$