Slope of a Line and Applications of Slope Section 3.1: Slope of a Line and Applications of Slope

Algebraically Verbally Numerical Example 3.1 Lecture Guide: Slope of a Line and Applications of Slope Objective 1: Determine the slope of a line. Slope of a Line Through and Algebraically Verbally Numerical Example The slope of a line is the ratio of the change in y to the change in x.   A 1-unit change in x produces a 2-unit change in y. for For the points (2, – 1) and (3, 1), and reduces to:

Slope of a Line Through and Graphical Example 2 unit change in y 1 unit change in x

Calculate the slope of the line through each pair of points then graph a line that passes through the points. 1. (– 2, 7) and (3, 5)

Calculate the slope of the line through each pair of points then graph a line that passes through the points. 2. (1, – 8) and (7, – 3 )

Calculate the slope of the line through each pair of points then graph a line that passes through the points. 3. (– 5, 3) and (2, 3)

Calculate the slope of the line through each pair of points then graph a line that passes through the points. 4. (5, 3) and (5, – 2 )

Classifying Lines by Their Slopes Numerically Verbally m is positive The line slopes ______________ to the right. m is negative m is zero The line is ________________________. m is undefined

5. Calculate the slope of the line in the graph.

7. Determine the slope of the line in the graph.

9. Calculate the slope of the line containing the points in the table.

11. Complete the table so that the points all lie on a line having a slope .

13. For the equation (a) (b) Find the x-intercept. Find the y-intercept. (c) Use the points to determine the slope of the line.

Algebraically Verbally Objective 2: Use slopes to determine whether two lines are parallel, perpendicular, or neither. Parallel and Perpendicular Lines If l1 and l2 are distinct nonvertical* lines with slopes m1 and m2 respectively, then: Algebraically Verbally Graphically l1 and l2 are parallel because they have the ___________ slope. or l1 and l2 are perpendicular because their slopes are negative ______________. * Also note all vertical lines are parallel to each other, and all vertical lines are perpendicular to all horizontal lines. y y

14. (a) If l1 and l2 are parallel and then _______. (b) If l1 and l2 are perpendicular and then _______.

15. If l1 and l2 are perpendicular and m1= – 4 then m2 = _______. 16. If l1 and l2 are perpendicular and m1= 0, then m2 is _______________.

Determine whether the line that passes through the first pair of points is parallel to, perpendicular to, or neither parallel nor perpendicular to the line that passes through the second pair of points. 17. and and

Determine whether the line that passes through the first pair of points is parallel to, perpendicular to, or neither parallel nor perpendicular to the line that passes through the second pair of points. and 18.

Determine whether the line that passes through the first pair of points is parallel to, perpendicular to, or neither parallel nor perpendicular to the line that passes through the second pair of points. 19. (– 2, 5) and (0,1) (7, 3) and (6, 5)

Determine whether the line that passes through the first pair of points is parallel to, perpendicular to, or neither parallel nor perpendicular to the line that passes through the second pair of points. 20. (– 3, 4) and (1, 7) (0, – 6 ) and (3, – 2)

Determine whether the line that passes through the first pair of points is parallel to, perpendicular to, or neither parallel nor perpendicular to the line that passes through the second pair of points. 21. (– 3, 4) and (6, 4) (– 2 , 5) and (– 2, 0)

Determine whether the line that passes through the first pair of points is parallel to, perpendicular to, or neither parallel nor perpendicular to the line that passes through the second pair of points. 22. (– 3, 4) and (6, 4) (– 2, 1 ) and (3, 1)

23. Compute the missing values in the table. Change in x Change in y Slope −5 3 7 4 2 Undefined

Using the given point and slope, determine another point on the line and graph the line. 24. Through (0, – 3) with Point: ___________.

Using the given point and slope, determine another point on the line and graph the line. 25. Through (0, 2) with Point: ___________.

Using the given point and slope, determine another point on the line and graph the line. 26. Through (4, – 3) with m = 0. Point: ___________.

Using the given point and slope, determine another point on the line and graph the line. 27. Through (4, – 3) with an undefined slope. Point: ___________.

Objective 3: Calculate and interpret rates of change. 28. A local high school purchases a copy machine for $1200. Due to depreciation, the value of the machine decreases with time. The table below lists the value y of the copy machine after x months. (a) Determine the rate of change of the value with respect to time. Months Value $1200 6 $1050 12 $900 18 $750 24 $600 30 $450 36 $300

28. A local high school purchases a copy machine for $1200 28. A local high school purchases a copy machine for $1200. Due to depreciation, the value of the machine decreases with time. The table below lists the value y of the copy machine after x months. (b) Interpret the meaning of this value. (c) At this rate, how long after the copy machine was purchased will the machine have no value?