Linear Functions

Identifying Linear Functions

100

What is a function whose graph forms a straight line called?

linear function

200

What is the slope intercept form of a linear equation?

y=mx+b

300

James started off with 3 jelly beans in his basket and added 5 for every egg he found in the egg hunt. What is the equation to represent this situation, and define your variables

y=5x+3 x=# of eggs found y=# of jelly beans

400

Tell whether the set of ordered pairs satisfies a linear function. If so, what is the slope? (2,4), (5,3) (8,2), (11,1)

linear m= -1/3

500

Abby is tracking the progress of her plant's growth. Today the plant is 5 cm high and is growing 1.5 cm per day. What is the linear model? How tall will the plant be in 20 days. Define your variables!

y=1.5x+5 y=plant height x=days after first recorded height In 20 days it'll be 35 cm tall

Using Intercepts

100

What is the x-coordinate of the point where the graph intersects the x axis called?

What is the x intercept

200

Name a single point that lies on the function f(x)=4x-5 and has an x value of 0. (put answer in coordinate form)

(0,-5)

300

The graph of the equation y=2x+3 is plotted on the standard (x,y) coordinate plane. How would you explain the transformation of this graph into the graph y=2x+9

The graph moved up 6 units

400

For the equation 2x+y=8, find the y-intercept. Write answer as an ordered pair. 

(0,8)

500

For the equation, 3x+2y=12, find the y-intercept. Write as an ordered pair. 

(0,6)

Slope

100

In the standard (x,y) coordinate plane, the graph of an equation in the form y=mx+b with m<0 is a(n) ________ function A)Increasing linear B)Decreasing linear C)Increasing quadratic D)Decreasing quadratic E)Decreasing exponential

Decreasing linear

200

What is the slope of the equation y=1/3x+4?

m=1/3

300

Find the slope of the line that has (4,-2) and (-1,2) on it. 

m= -4/5

400

The coordinates below model a constant decrease in annual Beanie Baby sales. The x value is the year after launch and the y value is sales in thousands of dollars. Use the following values to calculate the amount, in dollars, of the decrease per year. (0,89) (1,82) (2,75) (3,68)

It decreases by $7,000 per year.

500

If f(x)=2x+2, what is f(x-2)?

f(x-2)=2(x-2)+2 f(x-2)=2x-2

Linear scenarios

100

In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.

y=5x+20 y=total cost x=# of months

200

Suppose that a bike rents for $4 plus $1.50 per hour. Write an equation in slope-intercept form that models this situation.

y=1.5x+4 x=hours y=total cost

300

Cameron is designing a calendar as a fund-raising project for math class. The cost of printing is $500, plus $2.50 per calendar. Write an equation in slope-intercept form that models the total cost of printing the calendars.

y=2.5x+500 x= # of calendars y=total cost

400

The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2015. Write an equation for the population (in millions)

y=.22x+17.4 x=number of years after 2010 y=population in millions

500

A salesman earns a salary of $30000 and a commission of 25% of his total sales for the year. Write an equation for his yearly income.

y=.25x+30000 or y=1/4x+30000 y=yearly income x=total sales

Using Linear models

100

y=12x+3 Evaluate for x=3

y=39

200

What value of x make 2x+5=13 true?

x=4

300

The original price of an item, x, is discounted by 20%. A coupon for $5.00 off is then applied to the discounted price. What is the equation for the final price of the item?

y=.8x-5

400

The CJHS Fishing Club is going on a fishing trip, and needs to rent a boat. "Float Your Boat" Rental charges $6 per hour per boat. "Fishing Etc" Rentals charges $2 per boat and $3 per hour. If they are going to use 1 boat for 3 hours, which is the better choice?

Fishing Etc

500

A store pays $400 for the licensing to sell Razorback shirts, as well as $3 for each shirt they get in inventory. The store then sells the shirts for $15. How many shirts must they sell to make a profit?

34 shirts