write an equation in slope- intercept form the slope-intercept equation is also referred to as...

WRITE AN EQUATION IN

SLOPE-INTERCEPT FORM

Write an equation in slope-intercept form

The slope-intercept equation is also referred to as

y = mx + b

linear equation, linearmodel or function

Write an equation in slope-intercept form

The slope, m, is also called the

m =y2 – y1______x2 – x1

coefficient

Write an equation in slope-intercept form The y-intercept, b, is also referred to as

the constant

y = mx + by = mx + b

Write an equation in slope-intercept form Example: The cost for 7 dance lessons

is $82. The cost for 11 lessons is $122.What is the cost per lesson?

The cost per lesson means slope which is what we need to find

Write an equation in slope-intercept form The cost for 7 dance lessons is $82.

The cost for 11 lessons is $122.

To find slope we need 2 ordered pairs

(7, 82), (11, 122)

Write an equation in slope-intercept form

Plug the points into the equation for slope

Reduce the top and bottom Simplify the fraction

m =y2 – y1______x2 – x1

(7, 82), (11, 122)

11 – 7 122 – 82

440

10

Write an equation in slope-intercept form

What’s the cost per lesson? The cost per lesson is $10

m = 10

Write an equation in slope-intercept form The cost for 7 dance lessons is $82.

The cost for 11 lessons is $122.

What is the flat fee?

The flat fee refers to the y-intercept which is what needs to be found

Write an equation in slope-intercept form

We know m, so plug it into the equation Plug in one of the points

Does it matter which point? Multiply 10(11) Subtract 100 from both sides

y = mx + by = 10x + b122 = 10(11) + b(11, 122)

122 = 110 + b-110 -100

12 = b

Write an equation in slope-intercept form

b is 12 so: The flat fee is $12

12 = b

Write an equation in slope-intercept form

Write a linear equation that relates the total cost, y, in terms of the lessons, x

Plug b back into the equation

y = 10x + by = 10x + 12

Write an equation in slope-intercept form Anjelita receives some money as a

birthday gift. She saves the money and adds more to it each week. After five weeks, she has saved $175. After 8 weeks she has $190.

How much does Anjelita save each week?

Write an equation in slope-intercept form Anjelita receives some money as a

birthday gift. She saves the money and adds more to it each week. After five weeks, she has saved $175. After eight weeks she has $190.

The question asks for slope, so find 2 points

(5, 175), (8, 190)

Write an equation in slope-intercept form

Plug the points into the equation for slope

Reduce the top and bottom Simplify the fraction

m =y2 – y1______x2 – x1

(5, 175), (8, 190)

8 – 5 190 – 175

3

155

Write an equation in slope-intercept form Anjelita receives some money as a

birthday gift. She saves the money and adds more to it each week. After five weeks, she has saved $175. After 8 weeks she has $190.

How much does Anjelita save each week?

m = 5, so Anjelita is saving $5 each week

Write an equation in slope-intercept form Anjelita receives some money as a

birthday gift. She saves the money and adds more to it each week. After five weeks, she has saved $175. After 8 weeks she has $190.

How much money did she receive for her birthday?

This question is asking for the b

Write an equation in slope-intercept form

Plug m into the equation Plug in one of the points Multiply Subtract 25 from both sides

(5, 175)y = mx + by = 5x + b175 = 5(5) + b175 = 25 + b

-25 -25150 = b

Write an equation in slope-intercept form

b = 150, so she received $150 for her birthday

150 = b

Write an equation in slope-intercept form Moesha feeds her dog the same amount

of dog food each day from a very large bag. On the 3rd day she has 44 cups left in the bag, and on the 11th day she has 28 cups left.How many cups of food does she feed her

dog a day?

Write an equation in slope-intercept form Moesha feeds her dog the same amount

of dog food each day from a very large bag. On the 3rd day she has 44 cups left in the bag, and on the 11th day she has 28 cups left.How many cups of food were in the bag

when she started?

Write an equation in slope-intercept form The cost of renting a van for one day

includes a flat rental fee plus a charge for each mile the van is driven while it is rented. A van that is driven 107 miles costs $97.15. a van that is driven 127 miles costs $106.15. What is the charge per mile?

Write an equation in slope-intercept form The cost of renting a van for one day

includes a flat rental fee plus a charge for each mile the van is driven while it is rented. A van that is driven 107 miles costs $97.15. a van that is driven 127 miles costs $106.15. What is the flat rental fee?

Write an equation in slope-intercept form A calling plan charges a rate per minute

plus a flat fee. A 10-minute call to the Czech Republic costs $3.19. a 15-minute call costs $4.29. Based on a linear model, predict the cost of a 22-minute call.

Write an equation in slope-intercept form In 1994, the average price of a new

domestic car was $16,930. in 2002, the average price was $19,126. based on a linear model, what was the approximate predicted average price for 2008?

Write an equation in slope-intercept form Robert bought an mp3 player for $125

and he pays a fee for each song he downloads. The linear equation that represents this situation is y = 2x + 125.What is the slope?What does it represent in this situation?

Write an equation in slope-intercept form Suppose you have already saved $75

toward the cost of a new iPod. You plan to save $10 more each week for the next several weeks. The linear equation that represents this situation is y = 10x + 75.What is the y-intercept?What does it represent in this situation?

Write an equation in slope-intercept form Ms. Chang’s class decides to participate

in a walkathon. Each participant in the walkathon must find sponsors to pledge a certain amount of money for each kilometer the participant walks. Alana’s sponsors will make a $5 donation plus $0.50 per kilometer. Write a linear equation that models this

situation

Write an equation in slope-intercept form Ms. Chang’s class decides to participate

in a walkathon. Each participant in the walkathon must find sponsors to pledge a certain amount of money for each kilometer the participant walks. Alana’s sponsors will make a $5 donation plus $0.50 per kilometer. How much would Alana collect from each

sponsor if she walks 8 km?

Write an equation in slope-intercept form Ms. Chang’s class decides to participate

in a walkathon. Each participant in the walkathon must find sponsors to pledge a certain amount of money for each kilometer the participant walks. Alana’s sponsors will make a $5 donation plus $0.50 per kilometer. What is the slope and what does it

represent?What is the y-intercept and what does it

represent?

Write an equation in slope-intercept form Leanne’s sponsors will pay $10

regardless of how far she walks.Write a linear equation that models this

situation.How much would Leanne collect if she

walks 8 km?What is the slope and what does it

represent?What is the y-intercept and what does it

represent?

Write an equation in slope-intercept form Gilberto’s sponsors will pay $2 per

kilometer?What a linear equation that models this

situation.How much would Leanne collect if she

walks 8 km?What is the slope and what does it

represent?What is the y-intercept and what does it

represent?