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

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

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

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)

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

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

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

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

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

More Graphing…

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

More Graphing…

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

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:

B

Am

Examples of Finding Slope Given Standard Form

5x – 4y = 8 15x + 3y = 17

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.

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.)