what is the equation of the line passing through...??

Question

1) (5,1) and (-6,3)

2) (4,3) and (-2,-4)

3) (4/5, -1) and (2/3, 1/2)

4) (2a, 3b+1) and (a - 6, 13b+5)


ps.. write the solution if possible

Answer 1

Slope Formula

m = y₂- y₁/ x₂- x₁

Ordered Pair

(5, 1)(- 6, 3)

m = 3 - 1 / - 6 - 5

m = 2 / - 11

m = - 2/11

- - - - - - - - --

Slope intercept form

y = mx + b

Ordered Pair

(- 6, 3)

3 = - 2/11(- 6) + b

3 = - (- 12/11) + b

3 = 12/11 + b

Transpose 12/11

3 - 12/11 = 12/11 + b - 12/11

3 - 12/11 = b

33/11 - 12/11

21/11 = b

- - - - - - - - - - -

The equation

y = - 2/11x + 21/11

Multiply both sides of the equation by 11

11(y) = - 11(2/11) + 11(21/11)

11y = - 2x + 21

Transpose 2x

2x + 11y = - 2x + 21 + 2x

2x + 11y = 21

Transpose 21

2x + 11y - 21 = 21 - 21

2x + 11y - 21 = 0

- - - - - - - - -s-

Answer 2

the general equation for a line in cartesian coordinate system is y=ax+b

1. you are given two points. from the first point: x = 5, y = 1, substitute in equation y=ax+b, you will get: 1=5a+b
from the second point x = -6, y = 3. you obtain the second equation: 3 = -6a + b. solve this system for a and b.