Question

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

Answer 1

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.

Answer 2

You have to put the same number on it