Question

Find the equation of the line that passes through (-2,-4), (1,-3)

is it

y=1/3x + -2
or
y=1/3x+-10/3

Answer 1

The two-point form of a straigth line:

y - y1= [ ( y2 - y1 ) / ( x2 - x1 ) ] ∙ ( x - x1 )

In this case:

x1 = - 2 , y1 = - 4

x2 = 1 , y2 = - 3

y - y1= [ ( y2 - y1 ) / ( x2 - x1 ) ] ∙ ( x - x1 )

y - ( - 4 ) = [ ( - 3 - ( - 4 ) ) / ( 1 - ( - 2 ) ) ] ∙ ( x - ( - 2 ) )

y + 4 = [ ( - 3 + 4 ) / ( 1 + 2 ) ] ∙ ( x + 2 )

y + 4 = ( 1 / 3 ) ∙ ( x + 2 )

y + 4 = x / 3 + 2 / 3

Subtract 4 to both sides

y + 4 - 4 = x / 3 + 2 / 3 - 4

y = x / 3 + 2 / 3 - 4

y = x / 3 + 2 / 3 - 12 / 3

y = x / 3 - 10 / 3