Answer:
y = -3/4x + 4 or 3x + 4y = 16
Step-by-step explanation:
Step 1
Find the slope of the given line
we have
3x + 4y = 15
Isolate the variable y
Subtract 3x from both sides
3x + 4y -3x = 15-3x
Divide by 4 both sides
y = -3/4x + 15/4
the slope of the given line is
m = -3/4
Step 2
Find the equation of the line that passes through the point and is parallel to the given line
we know that
if two lines are parallel, then their slopes are equal
The equation of the line into point-slope form is equal to
y - y₁ = m(x-x₁)
we have
m= -3/4
(x1,y1) = (8,-2)
substitute in the equation
y + 2= -3/4(x-8)
y = -3/4x + 6 - 2
y = -3/4x + 4 or 3x + 4y = 16
therefore
the answer is
y = -3/4x + 4
or
3x + 4y = 16
