what is a equation of a line through points (4,3) and (2,4)?

Question

find the equation for each line through the two points (4,3) and (2,4)?

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) = (4, 3) and (x₂, y₂) = (2, 4).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

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

⇒ m = - 1/2.

Now, the line equation is y = (- 1/2)x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (4, 3).

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

b = 3 + 2

⇒ b = 5.

The line equation required is y = (- 1/2)x + 5.