16. slope ab= slope ac= slope bc=

17. which slope in item 16 is the steepest?

18. is triangle abc a right triangle? if so show why.

19. write the equation of a line through c that is parallel to ab (or just give coordinates)

20. write the equation of a line through b that is perpendicular to ac.

The answer to your question is:

Step-by-step explanation:

Data

A (-2, 0)

B (2, 3)

C (5, -1)

Process

Slope AB    m = (3 - 0) / (2 + 2)

                  m = 3/4

Slope AC    m = (-1 - 0) / 5 + 2)

                      = -1 /7

Slope BC    m = (-1 -3)/ (5 - 2)

                      = -4/3

17. Which slope in item 16 is the steepest? __AC___

18. Is triangle ABC a right triangle? If so show why.  Yes, it's a right triangle because slope AB is perpendicular to slope AC, then they form an angle of 90°.    (3/4)(-4/3) = -1

19. Write the equation of a line through C that is parallel to AB (or just give coordinates)

slope = 3/4

point (5,-1)

                              (y - y1)= m(x - x1)

                               y + 1 = 3/4(x - 5)

                              y + 1 = 3/4x - 15/4

                              y = 3/4x - 15/4 -1

                              y = 3/4 x - 19/4

20. Write the equation of a line through B that is perpendicular to AC.

B (2, 3)

slope = 7

                           y - 3 = 7(x - 2)

                          y - 3 = 7x - 14

                          y = 7x - 14 + 3

                          y = 7x - 11