Question

write equation of each line in slope intercept form(-6, 2), (3,6)

Answer 1

Given points say (x1,y1) = (-6,2)

(x2,y2) =(3,6)

slope = 6-2/3-(-6)

= 4/9

Consider the slope is same to each equation.

Equation of a line through (-6,2) is y-2 = 4/9(x-(-6))

y-2 = 4/9(x+6)

9(y-2) = 4(x+6)

9y-18 = 4x+24

9y = 4x+24+18

Divide by 9 to each side.

9y/9 = 4x/9+42/9

y = (4/9)x+14/3

Equation to the line which is passes through (3,6)

y-6 = 4/9(x-3)

(y-6)9 = 4(x-3)

9y-54 = 4x-12

9y = 4x-12+54

Divide by 9 to each side.

9y/9 = 4x/9-12/9+54/9

y =  (4/9)x-4/3+6

y = (4/9)x+14/3

 

Answer 2

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Let the points are (x₁, y₁) = (- 6, 2) and (x₂, y₂) = (3, 6).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(6 - 2)/(3 - (-6))]

m  = [4/(3 + 6)]

⇒ m = 4/9.

Now, the line equation is y = (4/9)x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (- 6, 2).

2 = (4/9)(- 6) + b

b = 2 + (8/3)

b = (6 + 8)/3

⇒ b = 14/3.

The line equation in slope - intercept - form is y = (4/9)x + (14/3).