If the equation of a line is

Question

4
x
+
4
y
=
1
and the equation of a second line is
x
+
y
=
−
8
. Which of the following is true?
A.
Both lines intersect at point
(
0
,
−
8
)
.

B.
The lines are parallel.

C.
The lines share the same x-intercept.

D.
The lines are perpendicular.

Answer 1

To determine if the lines intersect, are parallel, have the same x-intercept, or are perpendicular, we can compare the slopes of the lines.

The equation of the first line is given as 4x + 4y = 1, and we can rearrange it to solve for y in terms of x: 4y = -4x + 1, y = (-4/4)x + 1/4, y = -x + 1/4. The slope of the first line is -1.

The equation of the second line is given as x + y = -8, and we can rearrange it to solve for y in terms of x: y = -x -8. The slope of the second line is -1.

Since both lines have the same slope of -1, they are parallel. Therefore, the correct answer is B. The lines are parallel.