Answer:
OPTION A: 2x + 3y = 5
Step-by-step explanation:
The product of slopes of two perpendicular lines is -1.
We rewrite the given equation as follows:
2y = 3x + 2
⇒ y = [tex]$ \frac{3}{2}x + 1 $[/tex]
The general equation of the line is: y = mx + c, where 'm' is the slope of the line.
Here, m = [tex]$ \frac{3}{2} $[/tex].
Therefore, the slope of the line perpendicular to the line given = [tex]$ \frac{-2}{3} $[/tex] because [tex]$ \frac{3}{2} \times \frac{-2}{3} = -1 $[/tex].
To determine the equation of the line passing through the given point and a slope we use the Slope - One - point formula which is:
y - y₁ = m(x - x₁)
The point is: (x₁, y₁) = (-2, 3)
Therefore, the equation is:
y - 3 = [tex]$ \frac{-2}{3} $[/tex](x + 2) $
⇒ 3y - 9 = -2(x + 2)
⇒ 3y - 9 = -2x - 4
⇒ 2x + 3y = 5 is the required equation.
Answer:
The first one is the right one.
2x+3y=5
Step-by-step explanation:
