SOLUTION
In this equation, we are meant to find the equation of the line that passes through the points ( 0, -6 ) and ( 8 , - 16 ).
( x 1 , y1 ) = ( 0, -6 )
( x 2 , y2 ) = ( 8 , - 16 )
We need to first get the gradient of the two points :
m = ( y2 - y 1 ) / ( x 2 - x 1 )
m = (- 16 - - 6 ) / ( 8 - 0)
m = -10 / 8
m = -5 / 4
Next , we use the equation of the line :
y - y1 = m ( x - x 1 )
y - - 6 = - 5/ 4 ( x - 0 )
y + 6 = - 5/ 4 x
Multiply through by 4 , we have :
4 ( y + 6 ) = -5 x
4y + 24 = -5 x
5 x + 4y + 24 = 0
CONCLUSION: The equation of the line is 5 x + 4y + 24 = 0.