To find:determinethe error in the given graph drawn by a student.
Explanation of Solution
Given information:
Given graph is as follows
Conditions given in the graph are
The graph plotted for equation (i), (ii) and (iii) are correct; however the shaded portion is incorrect.
Shaded portion is to be drawn between two lines such that it satisfies all the condition.
According to equation (i) solution should contain the area such that
This is done by drawing a line at
According to equation (ii),
As per this condition the solution should have area such that at any point y co-ordinate of that point is greater than
In the graph plotted by student, condition (ii) is not fulfilled.
According to eqaution (iii),
It can be solved by converting this equation into slope-intercept equation of line which is
This becomes an equation of a line which a slope of
In the graph plotted by the student the line has positive slope which is incorrect.
Therefore conditon (iii) is also not fulfilled.
The correctly plotted graph would be
And the correctly shaded graph as solution will be
Conclusion:
Therefore, the portion shaded as gray should be a part of solution.
Chapter 6 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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