Answer:
Step-by-step explanation:
Equation of the line y = mx + c
The new line is perpendicular to 2x - 3y = -5
- 3y = - 5 - 2x
3y = 2x + 5
y =[tex]\frac{2x}{3} + \frac{5}{3}[/tex]
Since the lines are perpendicular to each other : [tex]m_{1} . m_{2} = -1[/tex]
where [tex]m_{1} \ slope \ of \ the \ given \ line \ and \ m_{2} \ slope \ of \ the \ new \line\\[/tex].
Slope of the given line
[tex]m_{1} = \frac{2}{3}[/tex]
Slope of the new line
[tex]\\\frac{2}{3}.m_{2} = -1\\ m_{2} = -1 . \frac{3}{2} = \frac{-3}{2}[/tex]
The equation to the new line passing through (-4, -3) and perpendicular to 2x - 3y = -5
[tex](y - y_{1}) = m_{2}(x-x_{2} )\\\\(y - (-4)) = \frac{-3}{2}(x - (-3)) \\\\(y + 4) = \frac{-3}{2} (x+ 3)\\\\2(y +4) = -3(x+3)\\\\2y + 8 = -3x -9 \\\\2y = -3x - 9 -8\\\\y = \frac{-3x}{2} - \frac{17}{2}[/tex]
