Find the equation of a straight line that passes through the points (6, −2) and (−12, −14) .

y = 2/3x - 6

Step-by-step explanation:

The equation of a line is

y = mx + c

Step 1: find the slope

m = y2 - y1 / x2 - x1

Given two points

( 6 , -2) ( -12 , -14)

x1 = 6

y1 = -2

x2 = -12

y2 = -14

m = ( -14 -(-2) / ( -12 - 6)

m = ( -14 + 2) / ( -12 - 6)

= -12/-18

Minus cancels minus

= 12/18

We can simply further using 6 to divide

= 2/3

m = 2/3

y = 2/3x + c

Step 2 : sub any of the two points given into the equation

let's pick ( 6 , -2)

x = 6

y = -2

y = 2/3x + c

-2 = 2/3(6) + c

-2 = 2 * 6 /3 + c

-2 = 12/3 + c

-2 = 4 + c

c = -2 - 4

c = -6

y = 2/3x - 6

The equation of the line is

y = 2/3x - 6