Question

Determine the slope of line (AB) and the slope of line (CD). Determine whether line (AB) and line (CD) are parallel, perpendicular, or just intersecting (neither). Points A and B line on the line y = 2/3x + 4. Points C and D line on the line 6x + 4y = 16.

Answer 1

The slopes are perpendicular

Explanation:

Points A and B line on the line y = 2/3x + 4.

This line is in the form

y = mx+b where m is the slope

The slope is 2/3

Points C and D line on the line 6x + 4y = 16.

Solve for y

6x+4y = 16

4y = -6x +16

Divide by 4

4y/4 = -6/4x + 16/4

y = -3/2 x +4

The slope is -3/2

The slopes multiply to -1

2/3 * -3/2 = -1

so they are perpendicular