3y + 6 = 2x

and

2y - 3x = 6

The lines represented by these equations are

A) parallel

B) the same line

C) perpendicular

D) intersecting but not parallel

3y + 6 = 2x

and

2y - 3x = 6

The lines represented by these equations are

A) parallel

B) the same line

C) perpendicular

D) intersecting but not parallel

Tutors, please sign in to answer this question.

San Jose, CA

Put each of the equations in the slope-intercept format y = mx+b where m is the slope and b is the y-intercept. A comparison of the slopes is needed to answer the question.

Equation 1:

3y + 6 = 2x

3y = 2x - 6

y = (2/3)x - 2

Equation 2:

2y - 3x = 6

2y = 3x - 6

y = (3/2)x - 3

The slope of the first line is 2/3 and the slope of the second is 3/2

Parallel lines have slopes which are the same.

Perpendicular lines have slopes which are negative reciprocals of each other.

The two equations are different so the lines are not identical.

Lines with different slopes will intersect.

Based on this, the correct answer is D.

- Math 11324
- Triangles 216
- Algebra 1 4375
- Quadrilateral 23
- Algebra 2 3735
- Geometry Word Problems 662
- Trigonometry 1662
- Prealgebra 186
- ANGLES 136
- Precalculus 1776