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=-(4)/(9)x-(8)/(9) \\ \text{The slope is}\Rightarrow m=-(4)/(9) \\ perpendicular\text{ slope}\Rightarrow m^(\prime)=(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=(9)/(4)(x+2) \\ 4y+8=9x+18 \\ 4y=9x+10 \\ y=(9)/(4)x+(5)/(2)(\text{Ans)} \\ 2. \\ The\text{ parallel equation is,} \\ y-y_1=m(x-x_1) \\ y+2=-(4)/(9)(x+2) \\ 9y+18=-4x-8 \\ 9y=-4x-26 \\ y=-(4)/(9)x-(26)/(9)(\text{Ans)} \end{gathered}`