. Find the slope of the line passing through the points (-3,5) and (7,6).
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Answer: See the attached image below for the dot plot
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Explanation:
The list
{50, 45, 24, 28, 27, 38, 21, 22, 23, 42, 41, 35, 37, 25, 43}
sorts to
{21, 22, 23, 24, 25, 27, 28, 35, 37, 38, 41, 42, 43, 45, 50}
Draw out a number line. Make sure to go as far down to 21 and as high as 50.
Then plot dots above the numbers 21, 22, 23,24,25,27,28, etc. Each item in the sorted list will get a dot overhead. In this case, there are no repeated items, so each stack is 1 dot high.
See the diagram below.
You may need to click on the magnifying glass if the diagram is either too small or distorted.
Part A:
The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B:
the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1
-2 <4 (-2) - 2
-2 <-10 (false)
inequality two
-2> = - (5/2) (- 2) - 2
-2> = 3 (false).
The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B:
the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1
-2 <4 (-2) - 2
-2 <-10 (false)
inequality two
-2> = - (5/2) (- 2) - 2
-2> = 3 (false).