Slope and y-intercept

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

y = mx + b Slope-intercept form

y = 6x + (–3) m = 6, b = –3

y = 6x – 3 Simplify.

Slope and y-intercept

Answer: Plot a point at the y-intercept, –3.

Use the slope of 6 or to find

another point 6 units up and1 unit right of the y-intercept.

Draw a line through these two points.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. x + y = 4

B. y = x – 4

C. y = –x – 4

D. y = –x + 4

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

Slope and a Point on the Line

Point-slope form

Write an equation in point-slope form of the line

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

graph the line.

Simplify.

Slope and a Point on the Line

Answer: Graph the given point (–10, 8).

Use the slope

to find another point 3 units down and 5 units to the right.

Draw a line through these two points.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Write an equation in point-slope form of the line

whose slope is that contains (6, –3).

A.

B.

C.

D.

Two Points

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

Step 1 First find the slope of the line.

Slope formula

x1 = 4, x2 = –2, y1 = 9, y2 = 0

Simplify.

Two Points

Step 2 Now use the point-slope form and either point to write an equation.

Distributive Property

Add 9 to each side.

Answer:

Point-slope form

Using (4, 9):

Two Points

B. Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3).

Step 1 First find the slope of the line.

Slope formula

x1 = –3, x2 = –1, y1 = –7, y2 = 3

Simplify.

Two Points

Step 2 Now use the point-slope form and either point to write an equation.

Distributive Property

Answer:

m = 5, (x1, y1) = (–1, 3)

Point-slope form

Using (–1, 3):

Add 3 to each side.y = 5x + 8

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

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

A.

B.

C.

D.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. y = 2x – 3

B. y = 2x + 1

C. y = 3x – 2

D. y = 3x + 1

B. Write an equation in slope-intercept form for a line containing (1, 1) and (4, 10).

Horizontal Line

Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form.

Slope formula

This is a horizontal line.

Step 1

Horizontal Line

Point-Slope form

m = 0, (x1, y1) = (5, –2)

Step 2

Answer:

Simplify.

Subtract 2 from each side.y = –2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Write an equation of the line through (–4, –8) and (–1, –6) in slope-intercept form.

A.

B.

C.

D.

Write Parallel or Perpendicular Equations of Lines

y = mx + b Slope-Intercept form

0 = –5(2) + b m = 5, (x, y) = (2, 0)

0 = –10 + b Simplify.

10 = b Add 10 to each side.

Answer: So, the equation is y = 5x + 10.

A. y = 3x

B. y = 3x + 8

C. y = –3x + 8

D.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Write Linear Equations

RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. A. Write an equation to represent the total first year’s 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.

A = mr + b Slope-intercept form

A = 525r + 750 m = 525, b = 750Answer: The total annual cost can be represented by

the equation A = 525r + 750.

Write Linear Equations

RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee.

Evaluate each equation for r = 12.

First complex: Second complex:A = 525r + 750 A = 600r +

200= 525(12) + 750 r = 12 =

600(12) + 200= 7050 Simplify. =

7400

B. Compare this rental cost to a complex which charges a $200 annual maintenance fee but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate?

Write Linear Equations

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

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. C = 25 + d + 100

B. C = 125d

C. C = 100d + 25

D. C = 25d + 100

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.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. first company

B. second company

C. neither

D. cannot be determined

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

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?