MTH 030 -- Elementary Algebra -- Exercise Solutions
Section:

19) Find the slope of the line passing through (2, 4) and (1, 3).
Solution:



The slope of the line passing through (2, 4) and (1, 3) is 1

20) Find the slope of the line passing through (1, 3) and (2, 5).
Solution:



The slope of the line passing through (1, 3) and (2, 5) is 2.

21) Find the slope of the line passing through (3, 4) and (2, 7).
Solution:



The slope of the line passing through (3, 4) and (2, 7) is -3.

22) Find the slope of the line passing through (3, 6) and (5, 2).
Solution:



The slope of the line passing through (3, 6) and (5, 2) is -2.

24) Find the slope of the line passing through (4, 3) and (7, 8).
Solution:



The slope of the line passing through (4, 3) and (7, 8) is .

26) Find the slope of the line passing through (6, -2) and (-3, 2).
Solution:



The slope of the line passing through (6, -2) and (-3, 2) is .

28) Find the slope of the line passing through (-1, -2) and (-10, -5).
Solution:



The slope of the line passing through (-1, -2) and (-10, -5) is .

30) Find the slope of the line passing through (-1, -12) and (6, -12).
Solution:
Observation that the two points have the same second coordinate implies that the line is horizontal and therefore has slope 0.
If you miss that observation then


The slope of the line passing through (-1, -12) and (6, -12) is 0.

32) Find the slope of the line passing through (-2, 8) and (-2, 15).
Solution:
Observation that the two points have the same first coordinate implies that the line is vertical and therefore its slope is undefined.
If you miss that observation then


The slope of the line passing through (-1, -12) and (6, -12) is undefined.

48) Sketch the graph of the line which passes through (-2, -1) with slope 4/3.

                                              

50) Sketch the graph of the line which passes through (2, -4) with slope 2/3.

                                              

51) Sketch the graph of the line which passes through (0, 0) with slope -4.

                                              

52) Sketch the graph of the line which passes through (0,0) with slope 5.

                                             

57) Find the slope of the bottom of the swimming pool as it drops off from the shallow end to the deep end as shown in the illustration below.

Solution:
It is helpful to superimpose a rectangular coordinate system over the drawing of the pool.


In view of this diagram the original question may be restated as: "What is the slope of the line through (5,-3) and (20, -9)?"


So the slope of the bottom of the pool is
Notice that if we consider rise over run, without a coordinate system we get the same slope. The rise is -6 (because it is "dropping off") and the run is 15 so that we get as the slope of the bottom of the pool.