Finding an equation of the line

Find an equation of the line that contains the given points.

1. (1,6) and (-2,-6)
2. (-3,12) and (1,-8)

1.) x1 = 1
y1 = 6
x2 = - 2
y2 = - 6

Slope, m = (y2 - y1) / (x2 - x1)

m = (- 6 - 6) / (- 2 - 1)
m = - 12 / - 3
m = 4

b = y1 - m(x1)
b = 6 - 4(1)
b = 6 - 4
b = 2

Equation of Line:

y = 4x + 2
¯¯¯¯¯¯¯¯¯

2.) x1 = - 3
y1 = 12
x2 = 1
y2 = - 8

m = (- 8 - 12) / [1 - (- 3)]
m = - 20 / (1 + 3)
m = - 20 / 4
m = - 5

b = 12 - [- 5(- 3)]
b = 12 - 15
b = - 3

Equation:

y = - 5x - 3
¯¯¯¯¯¯¯¯¯¯
 

To find the slope and equation

y=mx+b m is the slope

m= (y1)-(y2) / (x1)-(x2)= 6-(-6)/1-(-2)= 12/3= 4 or 4/1

pick a pair of coordinates (1,6)

y=6 m=4 x=1 b=unknown

y=mx+b 6=4(1)+b 6=4+b 6-4=b b=2

y=mx+b y=4x+2 this is the equation for the first set of pairs I hope that I helped you with the first set of coordinates. I am going to try and solve the next one tomorrow.

1) (1,6) and (-2,-6)

First, find the slope:

m = (y2 - y1) / (x2 - x1)
m = (-6 - 6) / (-2 - 1)
m = -12 / -3
m = 4

Write out what you know the equation will look like so far:
(remember, y = mx + b)

y = 4x + b

To solve for y, choose one of the points (I'll show it with (1,6) but it work with the other one too). Substitute the x value of the point (1) for x in the equation and the y value for the point (6) for y in the equation:

6 = 4(1) + b

Solve for b:
6 = 4 + b
b = 2

So the equation is:
y = 4x + 2

2) Basically the same exact process:

m = (-8 - 12) / (1 - (-3))
m = (-8 - 12) / (1 + 3)
m = -20 / 4
m = -5

Equation so far:
y = -5x + b

Substitute with the point (1, -8):
-8 = -5(1) + b

solve for b:
-8 = -5 + b
b = -3

The equation is:
y = -5x - 3