SLOPESLOPE

The ratio of the vertical change to The ratio of the vertical change to the horizontal changethe horizontal change

IN LAYMANIN LAYMAN’’S TERMS:S TERMS:

Wheelchair RampsWheelchair Ramps• Ramp steepness is Ramp steepness is

governed by the Americangoverned by the American’’s s with Disabilities ACT.with Disabilities ACT.

• ADA Accessibility Guidelines ADA Accessibility Guidelines for Buildings and Facilities for Buildings and Facilities (ADAAG) are located at: (ADAAG) are located at: http://www.access-board.gov/adaag/html/adaag.htm#4.8

How steep of a ramp should be acceptable for a person in a wheelchair?

Stairs are an excellent Stairs are an excellent example of slope example of slope

runrise

Most of us are familiar with associating ‘stairs’

with ‘slope’.

Do you have any questions about finding

the slope of stairs?

You can place a board over any set of stairs and get a ramp, but would the slope always be acceptable for

strollers and wheelchairs?

HOW ITHOW IT’’S FIGURED:S FIGURED:

STEEPNESS = ___________________VERTICAL CHANGEHORIZONTAL CHANGE

SLOPE (m) = ___________________Change in Y-axisChange in X-axis

**OR**

Using the Slope Formula Using the Slope Formula when given 2 endpointswhen given 2 endpoints

12

2

2

xy

m1322

y

m

This is an XLets make it our 1st X

212

24

1322

m12

12

x

yym

12

12

xxyym

This is a Y. Lets make it our 1st Y

Another X. It’s our 2nd one.

Another Y. Its our 2nd one. Lets plug it in and

solve for slope (m).

WORK TIME!WORK TIME!

Find the slope of a line that

contains points A(-2, 5) B(4, -5)

HEREHERE’’S HOW YOU SOLVE IT:S HOW YOU SOLVE IT:

SLOPE (m) = ___________________Change in Y-axisChange in X-axis

m of line AB = ___________________5 – (-5)-2 - 4

= ___________________10-6

= ___________53-

Use the following endpoints to Use the following endpoints to calculate slope with the given calculate slope with the given formula. Could these lines be formula. Could these lines be wheelchair ramps?wheelchair ramps?

Practice Problems:Practice Problems:

1.1. (4,6) (-2,3) (4,6) (-2,3) 2.2. (5,-7) (6,7)(5,-7) (6,7)3.3. (3,-2) (4,3)(3,-2) (4,3)12

12

xxyym

NOW TRY THESE ON YOUR NOW TRY THESE ON YOUR OWNOWN

Find the slope of a line that

contains each pair of points:

1. R(9, -2) S(3, -5)2. M(7, -4) N(9, 4)

Slope Slope • Slope is also known as a Slope is also known as a ““rate of rate of

changechange””..

• Rate of change describes how a Rate of change describes how a quantity changes over time.quantity changes over time.

ExampleExample• Between 1990 and 2000, annual Between 1990 and 2000, annual

sales of electronic games equipment sales of electronic games equipment increased by an average rate of 92.4 increased by an average rate of 92.4 million per year. In 2000, the total million per year. In 2000, the total sales were $1074.4 million. If sales sales were $1074.4 million. If sales increase at the same rate, what will increase at the same rate, what will the total sales be in the year 2010?the total sales be in the year 2010?

Answer:Answer:• Let our first (x,y) be (2000, 1074.40), which Let our first (x,y) be (2000, 1074.40), which

represents (time, value). The rate of change represents (time, value). The rate of change (slope) would be 92.4, and our second (x,y) would (slope) would be 92.4, and our second (x,y) would be (2010, Y).be (2010, Y).

• Therefore 92.4 = Therefore 92.4 = Y – 1074.4Y – 1074.4• 2010 – 20002010 – 2000• 92.4 = 92.4 = Y - 1074.4Y - 1074.4• 1010• 924 = Y – 1074.4924 = Y – 1074.4• 1998.4 = Y1998.4 = Y• Therefore the total sales would be projected to beTherefore the total sales would be projected to be• $1998.4 million.$1998.4 million.

If a line goes up from left to right, then the slope has to e positive

Conversely, if a line goes down from left to right, then the slope has to be negative

Horizontal lines have a slope of zero while vertical lines have no slope

HorizontalVertical

m = 0

m = no slope

Parallel Lines have the same Parallel Lines have the same slope.slope.• Postulate:Postulate:• Two nonvertical lines have the same Two nonvertical lines have the same

slope if and only if they are parallel.slope if and only if they are parallel.

Perpendicular lines have Perpendicular lines have opposite reciprocal slopes.opposite reciprocal slopes.• Postulate:Postulate:

• Two non-vertical lines are Two non-vertical lines are perpendicular if and only if the perpendicular if and only if the product of their product of their

• slopes is -1.slopes is -1.

ExampleExample• Determine whether line FG and line Determine whether line FG and line

HJ are perpendicular, parallel or HJ are perpendicular, parallel or neither.neither.

• F (1,-3) G(-2,-1) H(5,0) J(6,3)F (1,-3) G(-2,-1) H(5,0) J(6,3)

• F(4,2), G(6,-3) H(-1,5) J(-3,10)F(4,2), G(6,-3) H(-1,5) J(-3,10)

AnswersAnswers• NeitherNeither

• ParallelParallel

True or False??True or False??

ALL HORIZONTAL LINESHAVE THE SAME SLOPE

TWO LINES MAY HAVE TWO LINES MAY HAVE THE SAME SLOPETHE SAME SLOPE

A LINE WITH A SLOPE OF 1PASSES THROUGH THE ORIGIN

THE ANSWERS!THE ANSWERS!

#1: All horizontal lines have the same slope. TRUE#2: Two lines may have the same slope. TRUE

#3: A line with a slope of 1 passes through the origin. FALSE