Question

parallel/perpendicular line through a point (mc)
question
find the equation of a line parallel to ( 4x - 4y = 24 ) that passes through the point ( (7, -4) ).
answer
( y = x - 6 )
( y = -x - 6 )
( y = x - 11 )
( y = -x - 11 )

Explanation:

Step1: Rewrite to slope-intercept form

Start with the given line:
$4x - 4y = 24$
Subtract $4x$ from both sides:
$-4y = -4x + 24$
Divide by $-4$:
$y = x - 6$
The slope of this line is $m=1$. Parallel lines have equal slopes, so the new line also has $m=1$.

Step2: Use point-slope formula

Point-slope form: $y - y_1 = m(x - x_1)$
Substitute $m=1$, $x_1=7$, $y_1=-4$:
$y - (-4) = 1(x - 7)$
Simplify:
$y + 4 = x - 7$

Step3: Solve for y

Subtract 4 from both sides:
$y = x - 7 - 4$
$y = x - 11$

Answer:

$y = x - 11$