Question

Which equation is in point-slope form and depicts the equation of this line?

a) ( y + 4 ) + - 1/3 ( x + 1 )
b) ( y - 1 ) = - 1/3 ( x - 2 )
c) ( y - 4 ) + - 5/3 ( x - 1 )
d) ( y+ 4 ) + 5/3 ( x + 1 )

Answer 1

we know
in the graph two points
point 1 (2,1)  and point 2 (-1,-4)
the equation in point-slope form is ----------------> (y-y1)=m(x-x1)

step 1
find the value of m
m=(y2-y1)/(x2-x1)----------> (-4-1)/(-1-2)--------> m=5/3

step 2
with the point (-1,-4)  and m=5/3
find the equation in point-slope form
(y-(-4))=(5/3)*(x-(-1))-------------> (y+4)=(5/3)(x+1)

the answer is the option d) ( y+ 4 ) =+ 5/3 ( x + 1 )