Let us Represent the Line A in the Standard form : y = mx + c
where : m is the Slope of the Line and c is the y-intercept
Given : Equation of Line A is 2x + 3y = 10
[tex]\bf{\implies y = \frac{-2}{3}x + \frac{10}{3}}[/tex]
Comparing with the Standard form, We can notice that :
Slope of Line A [tex]\bf{= \frac{-2}{3}}[/tex]
We know that : Parallel lines have Same Slope
Given : Line A and Line B are Parallel
⇒ Slope of Line B [tex]\bf{= \frac{-2}{3}}[/tex]
Given : Line B passes through the Point (-6 , 8)
We know that : Equation of a Line passing through a Point (x₀ , y₀) and having Slope 'm' is given by : y - y₀ = m(x - x₀)
Here : x₀ = -6 and y₀ = 8 and Slope(m) [tex]\bf{= \frac{-2}{3}}[/tex]
Equation of Line B is :
[tex]\bf{\implies y - 8 = \frac{-2}{3}(x + 6)}[/tex]
⇒ 3y - 24 = -2x - 12
⇒ 2x + 3y = 12
