Remediation

Slope

run

rise

xx

yym

12

12

Slope

Find the slope of a line given two points: (3, 4) and (7, 8).

m = (8 – 4)/(7 – 3) = 4/4 = 1 The slope is 1.

Y-intercept

The y-intercept is where the line crosses the y axis.

It is written (0, #) since the x part of the point is 0 when it goes across the y axis.

To find the y-intercept in a line, put in 0 for x and solve for y.

Y-intercept

Given the line y = 2x + 5, find the y intercept.

First substitute in 0 in place of x. y = 2(0) + 5 Now solve for y y=5 This the y-intercept. (0, 5)

X-intercept

The x-intercept is where the line crosses the x axis.

It is written (#, 0) since the y part of the point is 0 when it goes across the x axis.

To find the x-intercept in a line, put in 0 for y and solve for x.

X-intercept

Given the line y = 2x + 5, find the x intercept.

First substitute in 0 in place of y. 0 = 2x + 5 Now solve for x -5 = 2x -5/2 = x This the x-intercept. (-5/2, 0)

Assignment:Find the slope of the line that passes through the points:

1)(-5, 3) and (0, 0)

2)(-3, 7) and (5, -3)

3)(-3, 8) and (-3, -4)

4)(13.5, 6) and (-11, 6)

0.4

.34

5.2

5

3.1

m

undefinedism

Click on picture for examples worked out

Image from: //upload.wikimedia.org/wikipedia/commons/c/ce/ChilkootPass_Slope.jpg

Assignment, continued

Find the equation of the line that passes through:

5) (6, 4) and m =

6) (-2, 7) and m =

3

2

5

3

6

35

5

3.6

3

2.5

xy

xy

Start with y=mx + b

Assignment, continued

Find the equation of the line that passes through the points:

7) (-8, -6) and (0, -6)

8) (1, -6) and (7, -4)

9) (-8, 3) and (0, 0)

10) (17.5, -9) and (17.5, 13)

5.17.108

3.9

3

19

3

1.8

6.7

x

xy

xy

y

Click on picture for examples worked out

Image from: http://commons.wikimedia.org/wiki/File:Artificial_ski_slopes.JPG

Graphing Lines

When a line is in slope intercept form, y=mx + b, you can graph by using the slope and the intercept.

Start by labeling your m (slope) and b (y-intercept).

Plot the b and move (rise/run) for the slope.

Rise

Run

Graphing Linesy= 2x + 4y= 2x + 4

Examples A 6-inch scented candle

burns at a rate of 0.1 inches each hour.

Starting at 6 inches= y-intercept, Decrease 0.1= slope -0.1

Let x=hours that the candle burns, y=height of the candle

*EQ: y=-0.1x+6 *Notice that the slope is negative because the candle height is decreasing as it burns!

*Q: How many hours has the candle burned if it is now 3.4 inches tall?

A: Use y=3.4, so 3.4=-

0.1x+6

-2.6=-0.1x, so x = 26 hours the candle burned

A national park has 8000 deer. It is estimated that the deer population will increase by 70 deer each year thereafter.

Starting 8000 = y-intercept, Increase 70 = slope

Let x=years from now, y=total deer in park

*EQ: y=70x+8000

*Q: How many deer will be in the park in 5 years?

A:Use x=5, so y=70(5)+8000=8350 deer in 5 years

Find the intercepts (page will check your answers)

http://www.algebrahelp.com/worksheets/view/graphing/intercepts.quiz

Interactive Slope Slider

http://www.shodor.org/interactivate/activities/SlopeSlider/

Slope Quiz

http://cs.selu.edu/~rbyrd/math/slope/slo_ty.html

Practice

Remediation LinksOverview

http://www.mathopenref.com/coordlineintro.html

Slope

http://www.mathopenref.com/coordslope.html

Point-Slope Form

http://www.mathopenref.com/coordequationps.html

Slope-Intercept Form

http://www.mathopenref.com/coordequation.html