(m) slope - Polk County School District · 2018-08-30 · SlopeIntercept Form.notebook 7 October...

SlopeIntercept Form.notebook

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October 01, 2014

SlopeIntercept Form

5 4 3 2 1 0 1 2 3 4 5

5

4

3

2

1

1

2

3

4

5

x

y

(b) yintercept

(m) slope

One way to write a linear equation is in SlopeIntercept Form


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October 01, 2014

The slope is always the change of output (y) divided by the input (x). It is also described as "rise over run".

It is the variable "m" in the y =mx + b or slopeintercept form.

SLOPE (m)SLOPE (m)Constant Rate of ChangeConstant Rate of Change

Slope

Slope

Slope Slope

NO SlopeNO Slope

SlopeSlope

NO SlopeNO Slope

NO SlopeNO Slope

The slope is always the change of output (y) divided by the input (x). It is also described as "rise over run".

It is the variable "m" in the y =mx + b or slopeintercept form.


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October 01, 2014

YINTERCEPTYINTERCEPTThe intersecting point on the yaxisThe intersecting point on the yaxis

b

b

bb

bb

b"b"

The yintercept is always on the yaxis. It is the

variable "b" in the y =mx + b or slopeintercept form.


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October 01, 2014

variablex axis

independent input (x)run( x, )domain

variablex axis

independent input (x)run( x, )domainy2 y1

x2 x1y2 y1x2 x1

(y = mx + b)(y = mx + b)

coefficientKROC

(k in direct variation)

ROC(constant rate of change)

ryse per runslope

coefficientKROC

(k in direct variation)

ROC(constant rate of change)

ryse per runslope

SLOPE YINTERCEPT FORMSLOPE YINTERCEPT FORM

y = +m x by m x bvariabley axis

dependent output (y)

ryse( ,y)range

variabley axis

dependent output (y)

ryse( ,y)range

constantyintercept(0,b) or (0,y)intersection on y axis

flat feeconstant numberno rate attached

constantyintercept(0,b) or (0,y)intersection on y axis

flat feeconstant numberno rate attached


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October 01, 2014

y2 y1x2 x1y2 y1x2 x1

(y = mx + b)(y = mx + b)SLOPE YINTERCEPT FORMSLOPE YINTERCEPT FORM

y = +m x by m x b


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October 01, 2014

SLOPE YINTERCEPT FORMSLOPE YINTERCEPT FORM

Identify the slope and yintercept of the equationy = 4x + 3 m = 4 b = 3

(0,3)y = 4x + 3

y = x 6 m = 1 b = 6 (0,6)y = 1x 6

(y = mx + b)(y = mx + b)

Find the "m" & "b" values from the y = mx + b form


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October 01, 2014

1) Find where the line crossesthe y axis = "b" 2) Find another point on the line (fit perfect in middle of the intersection of x and y axis)3) Count the ryse 4) Count the run5) Divide the ryse/run (m)and simplify 6) Look for the + or direction of the line and insert in front of m7)Substitute m & b into the y = mx + b form


Given the graph, write the slopeintercept form

44

1

1

4

(0,1)

y intercept"b"4

ryse

ryse

+1

run

run

y = 4x + 1y = 4x + 1

+

+


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October 01, 2014

1) Find where the line crossesthe y axis = "b" 2) Find another point on the line (fit perfect in middle of the intersection of x and y axis)3) Count the ryse 4) Count the run5) Divide the ryse/run (m)and simplify

6) Look for the + or direction of the line and insert in front of m7) Substitute m & b into the y = mx + b form y = x + 3y = x + 31

2



22

+4

+442

(0,3)


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October 01, 2014

PRACTICEPRACTICE

Identify the slope and yintercept of the equation

y = 3x 2

y = 7x + 9

y = x + 2

(y = mx + b)(y = mx + b)


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October 01, 2014

PRACTICEPRACTICE

m = 5 b = 9

m = 2 b = 8

m = b = 17

(y = mx + b)(y = mx + b)Given the slope and yintercept, write the equation


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October 01, 2014

PRACTICEPRACTICE(y = mx + b)(y = mx + b)



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October 01, 2014




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October 01, 2014




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October 01, 2014

1 Calculate the slope

2 Find the yintercept

3 Write the equation of the line

in the SlopeIntercept Form

Push the shade to find the answerHint:

Teacher will change the slope

and the yintercept and repeat

the question as many times

as the students need to practice.


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October 01, 2014

Draw a line through the point (1,2) with the slope of -3/2

First plot the point on a coordinate plane.

Find another point using slope -3/2(remember what does -3/2 as the slope mean?)

Draw a line through the points!


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October 01, 2014

Try this! Graph the line through the point (2,-3) with slope 5/4


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October 01, 2014

When given an equation such as y=mx+bslope is the coefficient to x. (m) ALWAYS!

Pull

Pull

This is a note page left blank so you can write in your own examples and have a class discussion about them.

Dependent/independent variable?


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October 01, 2014

y = 4x + 6

m = 4

What is the slope of the given equation (function) ?

y = 1/3x 9

m = 1/3


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October 01, 2014

y = x + 3/4

m = 1

4x + 2y = 164x = 4x + 162y = 4x + 162 2 2y = 2x + 8m = 2


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October 01, 2014

2x + y = 82x = 2x + 8y = 2x + 8m = 2

y = 2 + 5x

y = 5x 2m = 5


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October 01, 2014

How do you find slope if you are given a graph?

How do you find slope if you are given an equation?

What might you have to do to the equation first?

How do you find slope if given two points from the line?

What do the little 2's & 1's mean in the slope formula?

RECAP!


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October 01, 2014

1 2 3 4 5 6 7 8

2

3

4

5

6

7

8

x

yh

t

(0,8)

(8,7)The graph shows the height

of a candle as it burns. Find

the slope and the vertical

intercept of the graph. Write

an equation for the height

of the candle in Slope

Intercept Form.

Heigh

t (cm

)

Height (minutes)Move the rectangle to see the answer

Slope= = = 0.125

The graph crosses the vertical axis at (0,8). The vertical intercept is 8

Let h = the height of the candle in centimeters after it has been burning t minutes

An equation for the height of the candle is h = 0.125 t + 8

RealWorld Problem


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October 01, 2014

Check your knowledgeRemember: The equation of the line in the slope intercept form is

y = m x + b

*Grandal (2009).This test copied from ihs_graphing retrived from : http://www.longwood.k12.ny.us/longsmart.jhs.html


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October 01, 2014

(m) slope - Polk County School District · 2018-08-30 · SlopeIntercept Form.notebook 7 October...

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