Question

Which equation represents the line that passes through the points (6 -3) and (-4 -9)

Answer 1

Lets first find the slope:
(y₂-y₁)=m(x₂-x₁)
(-9-(-3)) = m(-4-6)
-6 = m(-10)
Isolate m:

`(-6)/(-10)` =
`(m(-10))/(-10)`
-10 and -10 cancels out

`(-6)/(-10)` = m

`(3)/(5)` = m

Now we know the slope, which is
`(3)/(5)`

The equations is
y = mx + c
Take any two coordinates from the given above

Im taking (6,-3)
Plug in those coordinates and the slope to the formula

-3 =
`(3)/(5)`(6) + c
-3 =
`(18)/(5)` + c
Isolate c
-3 -
`(18)/(5)` = c

`- (33)/(5)` = c
which gives us:
-6.6 = c

Now plug in the slope and c in the equation:

y =
`(3)/(5)`x+ (-6.6)
or
y =
`(3)/(5)`x +(-
`(33)/(5)`)

Answer 2

This answer will get deleted...but I do not have time to post the work on this one..

m= 3/5

b=-33/5


`y= (3)/(5) x+- (33)/(5)`

Thus, your equation.