Question

Use the linear equations to answer the question. Information y equals StartFraction 2 over 3 EndFraction x minus 3 y equals StartFraction negative 3 over 2 EndFraction x plus 2 Question Which statement about the lines is true? Answer options with 4 options A. The lines are the same. B. The lines are parallel. C. The lines are perpendicular. D. The lines intersect but are not perpendicular.

Answer 1

Answer:

C. The lines are perpendicular.

Step-by-step explanation:

Given the equation of the lines expressed as:

L1: y = 2/3 x - 3 and L2: y = -3/2 x +2

Comparing to the standard form of equation of a line y= mx+c

The slope of L1 is m1 = 2/3

The slope of line L2 is -3/2

Since their slope are not the same, therefore the lines are not parallel to each other.

For two lines to be perpendicular, the product of their slope is -1.

Let's check for both lines:

Check the product of their slope;

m1m2 =2/3 * -3/2

m1m2 = -6/6

m1m12 = -1

Since the product of their slope is -1, hence the lines are perpendicular to each other.

Option C is correct