Slope Lesson 2-3 Algebra 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.

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.

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.

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

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

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.

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.

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

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

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

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.

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

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

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.

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

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

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

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.)