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x - 4y = - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x - 4y = 4  ( subtract x from both sides )

- 4y = - x + 4 ( divide all terms by - 4 )

y = x - 1 ← in slope intercept form

with slope m =

Parallel lines have equal slopes, thus

y = x + c ← is the partial equation

To find c substitute (- 8, - 1) into the partial equation

- 1 = - 2 + c ⇒ c = - 1 + 2 = 1

y = x + 1 ← equation in slope- intercept form

Multiply through by 4

4y = x + 4 ( subtract 4y from both sides )

0 = x - 4y + 4 ( subtract 4 from both sides )

- 4 = x - 4y, that is

x - 4y = - 4 ← equation in stanfard form