Question

Write an equation for the line going thourgh the points (3,2),(-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) = (3, 2) and (x₂, y₂) = (-2, 4).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

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

⇒ m = -2/5.

Now, the line equation is y = (-2/5)x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (3, 2).

2 = (-2/5)(3) + b

b = 2 + (6/5)

b = (10 + 6)/5

⇒ b = 16/5.

The line equation in slope - intercept - form is y = (-2/5)x + (16/5).

The equation standard form is 2x + 5y = 16.