standard form passing through (-2,4) and (6,-1)

Question

write an equation in standard form of the line passing through each pair of points (-2,4) and (6,-1)

Answer 1

The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

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) = (6, -1).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(-1 - 4)/(6 - (-2))]

⇒ m = -5/8.

Now, the line equation is y = (-5/8)x + b.

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

4 = (-5/8)(- 2) + b

b = 4 - (5/4)

⇒ b = 11/4.

The line equation in slope - intercept - form is y = (-5/8)x + (11/4).

(- 5/8)x - y + (11/4) = 0

(- 5x - 8y + 22)/8 = 0

Therefore, the line equation is - 5x - 8y = - 22 .