Answer:
2x + 3y - 4 = 0
Step-by-step explanation:
Equation of the line → 2x - 3y + 4 = 0
3y = 2x + 4
y = [tex]\frac{2}{3}x+\frac{4}{3}[/tex]
Slope of this line 'm' = [tex]\frac{2}{3}[/tex]
y-intercept of this line → y = [tex]\frac{4}{3}[/tex] Or [tex](0, \frac{4}{3})[/tex]
Let the equation of the line is,
y = m'x + b'
By the property of perpendicular lines,
m × m' = -1
[tex]\frac{2}{3}\times m'=-1[/tex]
m' = [tex]-\frac{3}{2}[/tex]
Equation of the perpendicular line will be,
y = [tex]-\frac{3}{2}x+b'[/tex]
Since this line passes through [tex](0, \frac{4}{3})[/tex],
[tex]\frac{4}{3}=-\frac{3}{2}\times 0+b'[/tex]
b' = [tex]\frac{4}{3}[/tex]
Therefore, equation of the perpendicular line will be,
y = [tex]-\frac{2}{3}x+\frac{4}{3}[/tex]
3y = -2x + 4
2x + 3y - 4 = 0
