Math 71

1. Math 71 2.5 – The Point-Slope Form of the Equation of a Line

2. Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line.

3. Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line.

4. Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line.

5. Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line. point-slope form

6. Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line. point-slope form

7. Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line. point-slope form point

8. Suppose we know a point on a line is , and the slope of that line is . Then any other point on the line must satisfy the following equation: We can rewrite this to get the _________________________ of the equation of a line: If we know a ____________on a line, and the ___________of the line, we can use point-slope form to get an equation of the line. point-slope form point slope

9. Ex 1.Write the point-slope form of the equation of the line with slope 3 that passes through the point Now write the equation in slope-intercept form. Ex 2.A line passes through the points and . Find an equation of the line in point-slope form. Now write the equation in slope-intercept form.

10. Nonintersecting lines that lie in the same plane are called __________________________.

11. Nonintersecting lines that lie in the same plane are called __________________________. parallel lines

12. What can you say about the slopes of parallel lines? If two lines have the same slope, are they guaranteed to be parallel?

13. What can you say about the slopes of parallel lines? If two lines have the same slope, are they guaranteed to be parallel? They’re the same.

14. What can you say about the slopes of parallel lines? If two lines have the same slope, are they guaranteed to be parallel? They’re the same. Yes!

15. Ex 3.Write an equation of the line passing through and parallel to the line whose equation is . Express the equation in point-slope form.

16. Lines that intersect at a right angle () are called __________________________________.

17. Lines that intersect at a right angle () are called __________________________________. perpendicular lines

18. What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

19. What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

20. What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

21. What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

22. What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes?

23. What is the slope of line m? What is the slope of line n? What happens when you multiply the slopes? Slopes of perpendicular lines are negative reciprocals

24. In general, product of slopes of two nonvertical perpendicular lines is ________. In other words, slopes of two nonvertical perpendicular lines are _____________________________. For example, if a line has slope , then any perpendicular line will have slope ______.

25. In general, product of slopes of two nonvertical perpendicular lines is ________. In other words, slopes of two nonvertical perpendicular lines are _____________________________. For example, if a line has slope , then any perpendicular line will have slope ______.

26. In general, product of slopes of two nonvertical perpendicular lines is ________. In other words, slopes of two nonvertical perpendicular lines are _____________________________. For example, if a line has slope , then any perpendicular line will have slope ______. negative reciprocals

27. In general, product of slopes of two nonvertical perpendicular lines is ________. In other words, slopes of two nonvertical perpendicular lines are _____________________________. For example, if a line has slope , then any perpendicular line will have slope ______. negative reciprocals

28. Ex 4.Find the slope of any line that is perpendicular to the line whose equation is .

29. Ex 5.Write the equation of the line passing through and perpendicular to the line whose equation is . Express the equation in point-slope form and slope-intercept form.

30. Summary point-slope form: parallel same slope(also two vertical lines are parallel) perpendicular slopes are negative reciprocals(also, vertical and horizontal lines are perpendicular)