Question

line A and line B are parallel. If line A is 2x + 3y =10, what is the equation for line B if it passes through the point (-6,8)

Answer 1

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

`\bf{\implies y = (-2)/(3)x + (10)/(3)}`

Comparing with the Standard form, We can notice that :

Slope of Line A
`\bf{= (-2)/(3)}`

We know that : Parallel lines have Same Slope

Given : Line A and Line B are Parallel

⇒ Slope of Line B
`\bf{= (-2)/(3)}`

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)
`\bf{= (-2)/(3)}`

Equation of Line B is :

`\bf{\implies y - 8 = (-2)/(3)(x + 6)}`

⇒ 3y - 24 = -2x - 12

⇒ 2x + 3y = 12