(a)
To write the equation of the line passing through the point
(a)
Answer to Problem 29E
The equation of the line parallel to
Explanation of Solution
Given:
Given a point
Concept Used:
Slope-Intercept form of a line:
Suppose that the equation of a line is given in the slope-intercept form:
Then, the
Point-Slope equation of a line:
Given the slope
Calculation:
Observe that the line
Compare
Now, parallel lines have the same slope.
Thus, the line parallel to
Now, to find the equation of the line passing through the point
Simplify the equation
Thus, the equation of the line parallel to
Conclusion:
The equation of the line parallel to
To write the equation of the line passing through the point
Answer to Problem 29E
The equation of the line perpendicular to
Explanation of Solution
Given:
Given a point
Concept Used:
Slope-Intercept form of a line:
Suppose that the equation of a line is given in the slope-intercept form:
Then, the
Slopes of perpendicular lines:
Suppose that two lines are perpendicular and that they have the slopes
Point-Slope equation of a line:
Given the slope
Calculation:
Observe that the line
Compare
Now, let the line perpendicular to
Then, it follows that:
Substitute
Now, to find the equation of the line passing through the point
Thus, the equation of the line perpendicular to
Conclusion:
The equation of the line perpendicular to
Chapter 0 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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