Write the equation of the line that passes through (2, 2) and (6, 3) in standard form.

Question

4x + 4y = 6

x + 4y = 12

4x + 4y = –12

x – 4y = –6

 

 

Answer 1

Point - slope form of the line equation : y - y₁ = m(x - x₁).

The standard form of the line equation is Ax + By = C.

Let the points are (x₁, y₁) = (2, 2) and (x₂, y₂) = (6, 3).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(3 - 2)/(6 - 2)]

⇒ m  = 1/4.

Now, the line equation in point slope form is y - y₁ = (1/4)(x - x₁).

Find the line equation by substituting any point in the line equation say (x₁, y₁) = (2, 2).

y - 2 = (1/4)(x - 2)

4y - 8 = x - 2

x - 4y = - 8 + 2

x - 4y = - 6.

Therefore, the standard form of the line equation passing through the given points is x - 4y = - 6.

Fourth option is the correct choice.