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Home > Documents > NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

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NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3. Slope-Intercept Form (of a line). Where m is the slope (in the form of a fraction) b is the y-intercept x & y are points on the line in the form (x, y). - PowerPoint PPT Presentation
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NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3
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Page 1: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Page 2: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Slope-Intercept FormSlope-Intercept Form(of a line)(of a line)

bmxy Where m is the slope (in the form of a fraction)

b is the y-intercept

x & y are points on the line in the form (x, y)

Page 3: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3.

Answer: The slope-intercept form of the equation of the line is

Slope-intercept form

Page 4: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4.

Your Turn:

Page 5: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Point-Slope Form Point-Slope Form (of a line)(of a line)

)( 11 xxmyy Where:

And (x, y) never get replaced.

Page 6: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Answer:

Write an equation in point-slope form of the line

whose slope is that contains (–10, 8).

Simplify.

Point-slope form

Page 7: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Write an equation in point-slope form of the line

whose slope is that contains (6, –3).

Your Turn:

Page 8: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0).

Find the slope of the line.

Slope formula

Simplify.

Page 9: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Example 4-3bExample 4-3b

bmxy

b 49 23

b69

Now use the slope-intercept form and either point to write an equation.

Slope-intercept form

Fill in m & b.

Using (4, 9):

Solve for bb3

323 xy

Page 10: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

OR Using (–2, 0):

Answer:

bmxy

b 20 23

b 30

Slope-intercept form

Fill in m & b.

Solve for bb3

323 xy

(–2, 0)

Page 11: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8).

Answer:

Page 12: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Write an equation in slope-intercept form for a line containing (-2, 4) and (6, -2).

Answer:

Page 13: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Write an equation in slope-intercept form for a line containing (-2, 4) and (-2, -2).

Page 14: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Example 4-4aExample 4-4aWrite an equation in slope-intercept form for a line containing (1, 7) that is perpendicular to the line

the slope

of a line perpendicular to it is 2.

bmxy

b 127

b27

Slope-intercept form

Fill in m & b.

Solve for bb5

52 xy

)7 ,1( ,2m

Page 15: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Write an equation in slope-intercept form for a line containing (4, 1) that is perpendicular to the line

44 xy

Your turn:

Answer:

Page 16: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Write an equation to represent the total annual cost A for r months of rent.

For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750.

Answer: The total annual cost can be represented by the equation

Slope-intercept form

Page 17: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Compare this rental cost to a complex which charges a $200 security deposit but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate?

First complex: Second complex:

Simplify.

Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.

Page 18: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

Answer:

RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit.

a. Write an equation to represent the total cost C for d days of use.

b. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate?

Answer: The first company offers the better rate. Nine days cost $325 instead of $365.

Page 19: NM Standards AFG.A.6, AFG.B.3, AFG.B.8, AFG.C.4, AFG.C.7, AFG.C.9, AFG.C.10, AFG.C.12, GT.B.3

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