32.3k views
7 votes
Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting

(intersect at just one point), or coinciding (intersect at all points)?
y = 4x + 12, x + 4y = 32
O perpendicular
O coinciding
O intersecting
O parallel

2 Answers

1 vote

Final answer:

The given lines represented by the equations y = 4x + 12 and y = (-1/4)x + 8 are perpendicular to each other as their slopes are negative reciprocals.

Step-by-step explanation:

We need to determine if the lines represented by the equations y = 4x + 12 and x + 4y = 32 are parallel, perpendicular, intersecting, or coinciding. To do this, we should first express the second equation in slope-intercept form, just like the first one, which is y = mx + b where m is the slope and b is the y-intercept.



Rewriting the second equation, we get:

  • x + 4y = 32
  • 4y = -x + 32
  • y = (-1/4)x + 8



The line represented by y = 4x + 12 has a slope of 4, and the line represented by y = (-1/4)x + 8 has a slope of -1/4. Since the slopes are negative reciprocals of each other, the lines are perpendicular and they intersect at a 90 degree angle.

User Jared Mackey
by
7.3k points
7 votes
You have to put the same number on it
User Capoeira
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories