Question

Please help me do this question I have a test soon!

Answer 1

Answer:

2x + 3y - 4 = 0

Step-by-step explanation:

Equation of the line → 2x - 3y + 4 = 0

3y = 2x + 4

y = $\frac{2}{3}x+\frac{4}{3}$

Slope of this line 'm' = $\frac{2}{3}$

y-intercept of this line → y = $\frac{4}{3}$ Or $(0, \frac{4}{3})$

Let the equation of the line is,

y = m'x + b'

By the property of perpendicular lines,

m × m' = -1

$\frac{2}{3}\times m'=-1$

m' = $-\frac{3}{2}$

Equation of the perpendicular line will be,

y = $-\frac{3}{2}x+b'$

Since this line passes through $(0, \frac{4}{3})$,

$\frac{4}{3}=-\frac{3}{2}\times 0+b'$

b' = $\frac{4}{3}$

Therefore, equation of the perpendicular line will be,

y = $-\frac{2}{3}x+\frac{4}{3}$

3y = -2x + 4

2x + 3y - 4 = 0