Question

Find the equation of the line passing through the points (6,2)(10,6)

Answer 1

Slope-intercept form: y= mx + b (m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y))

To find the slope, use the slope formula and plug in 2 points:

`m=(y_2-y_1)/(x_2-x_1)`

(x₁ , y₁) = (5, 2)

(x₂ , y₂) = (10, 6)

`m=(6-2)/(10-5) =(4)/(5)`

`y=(4)/(5)x+b` To find b, plug in a point into the equation (5, 2)

`2=(4)/(5)(5)+b`

2 = 4 + b

-2 = b

`y=(4)/(5)x -2`

Answer 2

y = 4/5x -2

Explanation:

equation of a line passing through two points is given by

y - y₁ = m (x - x₁), where m = (y₂ - y₁) / (x₂ - x₁)

y₂ = 6, y₁ = 2

x₂ = 10, x₁ =5

m = (6-2)/(10-5)

m = 4/5

y - 2 = 4/5 (x - 5)

multiply both sides by 5

5(y -2) = 4(x - 5)

5y -10 = 4x -20

5y = 4x -20 +10

5y = 4x -10

divide through by 5

y =4/5x -2