find the equation of the line that goes through the points (-2,22) and (5,85)

Question

Find the equation of the line that goes through (-2,22) and (5,85).

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, 22) and (x₂, y₂) = (5, 85).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(85 - 22)/(5 + 2)]

m = 63/7

⇒ m = 9.

Now, the line equation is y = 9x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (5, 85).

85 = (9)(5) + b

b = 85 - 45

⇒ b = 40.

The required line equation is y = 9x + 40.