
Concept explainers
a.
To evaluate the given statement.
a.

Answer to Problem 4.1.4P
The two lines are not perpendicular
Explanation of Solution
Given information:
One line goes through (-6, -2) and (2, 10)
Other graph is
Formula Used:
Product of slopes of two perpendicular slope is -1.
Equation of line,
Formula of slope is,
Calculation:
For the slope of line, substituting the value in slope formula,
So,
On solving,
Hence, slope is 1.5
Converting the graph equation in equation of line format,
Shift left-hand side values to right-hand side,
Cross-multiplying both sides,
On solving,
On solving,
Comparing it with the equation of line,
Slope is 1.5
Multiplying both the slopes,
On solving,
Since, the product of the two slopes is 2.25 and not -1.
Therefore, the two lines are not perpendicular.
Conclusion:The two lines are not perpendicular
b.
To evaluate the two lines
b.

Answer to Problem 4.1.4P
The given two lines are not parallel
Explanation of Solution
Given information:
The line goes through (7, -10) and (3,-2)
Another line is
Formula Used:
Two parallel lines have the same slope (m).
Formula of slope is,
Equation of line is,
Calculation:
For the slope of line one, substituting the values in the slope formula,
So,
On solving,
Hence, the slope of line one is -2.
Converting the equation of line two in the form of
Shifting left- hand side value to right- hand side,
Comparing with
Hence, slope of line two is 2
Comparing the slopes of the two lines,
The slopes of the two lines are not equal as slope of line one is 2 and slope of line two is -2.
Therefore, the lines are not parallel
Conclusion:The given two lines are not parallel
c.
To identify the mistake in the statement.
c.

Answer to Problem 4.1.4P
The two lines are not parallel because the two lines have a common point.
Explanation of Solution
Given information:
Line1 goes through (1,-4) and (5,-6)
Line2 goes through (2,-7) and (5,-6)
Formula Used:
Two parallel lines do not intersect each other.
Calculation:
The point lines have a common point, that is (5,-6), hence the two lines intersect at that point.
Hence, the two lines are not parallel and Alonae is wrong.
Conclusion: The two lines are not parallel because the two lines have a common point.
Chapter ISG Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Basic Business Statistics, Student Value Edition
University Calculus: Early Transcendentals (4th Edition)
A First Course in Probability (10th Edition)
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