slope lesson 2-3 algebra 2. slope slope basically describes the steepness of a line if a line goes...

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SLOPE LESSON 2-3 Algebra 2

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Page 1: 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

SLOPELESSON 2-3

Algebra 2

Page 2: 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

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

Page 3: 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

Slope Formula

12

12

xx

yy

x

y

run

risemslope

In order to use that formula we need to know, or be able to find 2 points on the line

Page 4: 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

Procedure for Finding Slope

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

12

12

xx

yym

(-3, 7) and (4, -6)

Page 5: 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

Examples of Finding Slope

(4, -1.5) & (3, 2.5) (1/2, 2/3) & (5/6, 1/4)

Page 6: 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

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

Page 7: 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

Your Turn:

Find the slope of the line passing through each pair of points. Then Graph the line.

1.(-1, 4) and (1, -2)

2.(-2, -3) and (0, -5)

3.(5, -4) and (5, 6)

4.(2, -7) and (-3, -7)

Page 8: 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

Graphing a Line Given a Point and Slope

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

(-4, -3) and m = 2/3

12

12

xx

yym

Page 9: 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

More Graphing…

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

Page 10: 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

More Graphing…

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

Page 11: 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

Your Turn…

Graph the line passing through the point (-3, -1) with m = -3

Page 12: 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

Standard Form and Slope

If a line is in the form Ax + By = C, we can use the following formula to find the slope:

B

Am

Page 13: 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

Examples of Finding Slope Given Standard Form

5x – 4y = 8 15x + 3y = 17

Page 14: 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

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

Page 15: 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

Your Turn…

Graph the line through (2, -1) that is parallel to the line with equation 2x + 3y = 6.

Page 16: 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

Perpendicular Lines & Slope

The slopes of perpendicular lines are opposite reciprocals.

What is a opposite reciprocal?

Page 17: 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

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

Page 18: 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

Your Turn…

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

Page 19: 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

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.)