1. MATH 017 Intermediate Algebra S. Rook
Slope of a Line
MATH 017
Intermediate Algebra
S. Rook

2. Overview Section 3.4 in the textbook
Definition and properties of slope
Slope-intercept form of a line
Slopes of horizontal and vertical lines
Slopes of parallel and perpendicular lines

3. Definition and Properties of Slope

4. Definition and Properties of Slope
Slope (m): the ratio of the change in y (Δ y) and the change in x (Δ x)
Quantifies (puts a numerical value on) the “steepness” of a line
Given 2 points on a line, we can find its slope:

5. Definition and Properties of Slope (Example)
Ex 1: Find the slope of the line containing (7, -1) and (4, 3)

6. Definition and Properties of Slope (Example)
Ex 2: Find the slope of the line containing (-6, -8) and (-8, -12)

7. Sign of the Slope of a Line
To determine the sign of the slope, examine the line from left to right
Positive if the line rises
Negative if the line drops

8. Slope-Intercept Form

9. Slope-Intercept Form
Slope-intercept form: a linear equation in the form y = mx + b where
m is the slope
b is the y-coordinate of the y-intercept (0, b)
Remember, to utilize the slope-intercept form of a line, y must be ISOLATED

10. Slope-Intercept Form (Example)
Ex 3: Find the slope and y-intercept of
y = 7x + 3

11. Slope-Intercept Form (Example)
Ex 4: Find the slope and y-intercept of
4x – 5y = 25

12. Slope-Intercept Form (Example)
Ex 5: Find the slope and y-intercept of
2x + 8y = 10

13. Slopes of Horizontal and Vertical Lines

14. Slopes of Horizontal and Vertical Lines
Suppose we have a horizontal line y = 2
2 points on this line would be (a, 2) and (b, 2)
Applying the slope formula, we have a slope of 0
Thus, we can say ALL horizontal lines have a slope of zero
Suppose we have a vertical line x = -1
2 points on this line would be (-1, a) and (-1, b)
Applying the slope formula, we have an undefined slope
Thus, we can say ALL vertical lines have an undefined slope

15. Slopes of Horizontal and Vertical Lines (Example)
Ex 6: Graph and give the slope of the line
4x = 4

16. Slopes of Horizontal and Vertical Lines (Example)
Ex 7: Graph and give the slope of the line
-6y = 10

17. Slopes of Parallel and Perpendicular Lines

18. Slopes of Parallel and Perpendicular Lines
Parallel lines: two lines that have the SAME slope
Perpendicular lines: two lines that have OPPOSITE RECIPROCAL slopes
In other words, the product of the slopes is -1

19. Slopes of Parallel and Perpendicular Lines (Example)
Ex 8: Determine whether 2x – y = 6 and 4x + 8y = 4 are parallel, perpendicular, or neither.

20. Slopes of Parallel and Perpendicular Lines (Example)
Ex 9: Determine whether 3x + 5y = 2 and 8x + 2y = 6 are parallel, perpendicular, or neither.

21. Summary
After studying these slides, you should know how to do the following:
Understand the definition of slope and be able to apply the slope formula when given 2 points on a line
Apply the definition of the slope-intercept form of a line to extract the slope and the y-intercept
Be able to give the slope of a horizontal or vertical line
Determine whether pairs of lines are parallel, perpendicular or neither