linear equation for through (2,4) and (-1,3)

Question

What is the equation.

Answer 1

Slope - intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Let the points are (x₁, y₁) = (2, 4) and (x₂, y₂) = (- 1, 3).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(3 - 4)/(- 1 - 2)]

m =  - 1/- 3

⇒ m = 1/3.

Now, the line equation is y = (1/3)x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (2, 4).

4 = (1/3)(2) + b

b = 4 - (2/3)

b = (12 - 2)/3

⇒ b = 10/3.

The line equation required is y = (1/3)x + (10/3).