1. Slope Lesson 2-3
Algebra 2

2. Slope Slope basically describes the steepness of a line
If a line goes up from left to right, then the slope has to be positive
Conversely, if a line goes down from left to right, then the slope has to be negative
Beginning course details and/or books/materials needed for a class/project.

3. Slope Formula
In order to use that formula we need to know, or be able to find 2 points on the line
A schedule design for optional periods of time/objectives.

4. Procedure for Finding Slope
(-3, 7) and (4, -6)
To find the slope given two points:
Determine the values of x1, x2, y1, and y2
Substitute the value of each variable in the formula and solve
Simplify the fraction as much as possible
DO NOT write the fraction as a mixed number of a decimal
A list of procedures and steps, or a lecture slide with media.

5. Examples of Finding Slope
(4, -1.5) & (3, 2.5)
(1/2, 2/3) & (5/6, 1/4)

6. Horizontal & Vertical Lines
Horizontal lines have a slope of zero (when 0 is on top of a fraction)
Vertical lines have no slope (when 0 is under the fraction bar)
m = 0
m = no slope

7. Your Turn:
Find the slope of the line passing through each pair of points. Then Graph the line.
(-1, 4) and (1, -2)
(-2, -3) and (0, -5)
(5, -4) and (5, 6)
(2, -7) and (-3, -7)
Objectives for instruction and expected results and/or skills developed from learning.

8. Graphing a Line Given a Point and Slope
(-4, -3) and m = 2/3
To graph a line given a point on the line and the slope of the line:
Plot the given point on graph paper
From that point, use your slope to find another point on the line
Connect your points to draw the line
Example graph/chart.

9. More Graphing…
(2, -1) and m = 3
(-3, -4) and m = -3/2

10. More Graphing…
(-2, -1) and m = no slope
(1, 4) and m = 0

11. Graph the line passing through the point (-3, -1) with m = -3
Your Turn…
Graph the line passing through the point (-3, -1) with m = -3

12. Standard Form and Slope
If a line is in the form Ax + By = C, we can use the following formula to find the slope:
Relative vocabulary list.

13. Examples of Finding Slope Given Standard Form
5x – 4y = 8
15x + 3y = 17
Example graph/chart.

14. Parallel Lines & Slope Parallel lines have the same slope.
Graph the line through (-1, 3) that is parallel to the line with equation x + 4y = -4.
Find the slope of the line with the given equation
Plot the point you are given
Use the slope you found to graph another point
Draw a line through the points

15. Your Turn…
Graph the line through (2, -1) that is parallel to the line with equation 2x + 3y = 6.
Conclusion to course, lecture, et al.

16. Perpendicular Lines & Slope
The slopes of perpendicular lines are opposite reciprocals.
What is a opposite reciprocal?

17. Perpendicular Lines & Slope
Graph the line through (4, -2) that is perpendicular to the line with equation 3x – 2y = 6.
Find the slope of the line with the given equation
Find the opposite reciprocal of this slope
Plot the point you are given
Use the opposite reciprocal slope you found to graph another point
Draw a line through the points

18. Your Turn…
Graph the line through (-1, 5) that is perpendicular to the line with equation 5x – 3y = 3.

19. Answer this question in your warm-up book.
How does slope apply to the steepness of roads?
Include the following in your answer:
A few sentences explaining the relationship between the grade of a road (the amount a road rises divided by the horizontal distance of the road) and the slope of a line
A graph of y = 0.1x which corresponds to a 10% grade (The scale on your x- and y-axes should be the same.)