Question

With slope –1/4, passing through (-4, -1)

Answer 1

`y = -(1)/(4)x - 2`

Explanation:

i'm not sure if you're trying to find the equation of the line ?? but i'll assume that's the case and find the slope-intercept form equation of the line.

slope intercept form is
`y = mx + b`, where
`m` is the slope and
`b` is the y-intercept. since the slope is already identified, you can plug in
`-(1)/(4)` for
`m`.

• 
  `y = mx + b` ⇒
  `y = -(1)/(4)x+b`

plug in the
`x` and
`y` values from the coordinate pair that passes through the line, which is (-4, -1). you can start with either
`x` or
`y`, but i'm going to start with
`x`.

first, plug in
`-4` for
`x`.

• 
  `y = -(1)/(4)x+b` ⇒
  `y = -(1)/(4)(-4)+b`

now plug in
`-1` for
`y`.

• 
  `y = -(1)/(4)(-4)+b` ⇒
  `-1 = -(1)/(4)(-4)+b`

after plugging in all of the given values, the equation is now
`-1 = -(1)/(4)(-4)+b`, in which you need to solve for
`b`.

now it's time to solve! begin by multiplying
`-(1)/(4)(-4)` in order to simplify the right side of the equation.

• 
  `-(1)/(4)(-4) = 1`

you now have
`-1 = 1 + b`. subtract 1 from both sides of the equation. on the right side, it cancels itself out, leaving you with
`b`. on the left side of the equation, you now have
`-1 - 1`, which equals
`-2`.

therefore
`-2 = b`, or
`b = -2`.

now that you've solved for your
`b` value, plug it into your initial slope-intercept form equation!

• 
  `y = -(1)/(4)x + b` ⇒
  `y = -(1)/(4)x - 2`

if you want to check to make sure that the values are correct, plug (-4, -1) into your completed slope-intercept form equation. as you did in the beginning, plug in
`-4` for
`x` and
`-1` for
`y`.

• 
  `y = -(1)/(4)x - 2` ⇒
  `-1 = -(1)/(4)(-4) - 2`

begin simplifying by multiplying
`-(1)/(4)(-4)`.

• 
  `-1 = -(1)/(4)(-4) - 2` ⇒
  `-1 = 1 - 2`

subtract
`1 - 2`.

• 
  `-1 = 1 - 2` ⇒
  `-1 = -1`

since both sides of the equation are equal, that means your
`b` value of
`-2` is correct because it makes the equation true!

aaaand there you go! i hope this helps. have a great day! <3