find the equation of the line through this pair of points.

Question

(1,1) and (6,2).

 

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) = (1, 1) and (x₂, y₂) = (6, 2).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(2 - 1)/(6 - 1)]

⇒ m = 1/5.

Now, the line equation is y = (1/5)x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (1, 1).

1 = (1/5)(1) + b

b = 1 - (1/5)

⇒ b = 4/5.

The line equation required is y = (1/5)x + (4/5).