Linear Functions and Models

Morgan has $263.49 in her bank account.  She babysits two days each week.  Each time she babysits she earns $36.  She deposits all the money she earns into her bank account at the end of the week.  Which linear equation below best models the relationship between the total amount of money in Morgan's bank account(T) and the number of weeks(w) that have passed?

• T = 72w + 263.49

• T = 36w + 263.49

• T = 263.49w + 36

• w = 72T + 263.49

A local donut shop charged $6.50 for a dozen and provided a coupon in the newspaper for $1.50 off an order. Since the donut shop has gained popularity they have changed their coupon which now provides a discount of only half their original coupon's value. What is the equation that represents the value of a customer's order who uses the new coupon with their order?

• y = 6.50x - 0.75

• y = 6.50x + 0.75

• y = 6.50x - 1.50 - 0.75

• y = 5x - 0.75

Heather is a hairdresser and her customers pay $5 to reserve an appointment time and $12 for every hour Heather works on their hair style. As a back to school special she offers to lower her price per hour by $5. What equation represents the total amount paid to Heather, y, after x hours of hair styling?

• y = 5 + 12x

• y = 12x

• y = 7x + 5

• y = 12x + 12

Randy charges his tenants $400 each month to rent his houses plus $600 security deposit. In the new year, the property taxes increased on the area where he rents so as a result he must increase the rate of change by $25 to ensure his profits are not harmed. What equation best represents how much his tenants will now have to pay?

• y = 425x + 600

• y = 425 + 600x

• y = 400x + 625

• y = 400 + 625x

Michelle and her husband want to go skydiving! The equation, f(x) = 12000 - 125x, represents the height (in feet) of the skydivers, f(x), after x seconds of falling. Michelle and her husband are adrenaline junkies so they have asked to increase the starting jump height by 500 feet and will deploy their parachute late which will change their falling speed to 200 feet per second. What equation represents these changes?

• y = 12000 - 200x

• y = 12500 + 75x

• y = 12500 - 200x

• y = 12200 - 625x

Jeff has already read 50 pages of his book.  In 10 minutes he can read 8 pages.  If p represents the total number of pages he has read and m represents the number of minutes he reads, then which equation best models this situation?  If the book is 225 pages, will he finish the book in 3 hours?

• p = 4.2m + 50 and yes

• p = 1.25m + 50 and yes

• p = 0.8m + 50 and no

• p = 4.2m + 50 and no

Valley Video charges a $15 annual fee plus $3 per movie for rentals. Last year, Jennifer spent $99 at the video store. How many movies did she rent? Write the linear equation and solve for the number of movies.

• 15x + 3x = 99    and 6 movies

• 15x + 3 = 99 and 6 movies

• 3x + 15 = 99 and 28 movies

• 3x + 99 = 15 and 28 movies

A waitress ears $100 every week plus tips from customers.  She can only keep 75% of the tips that she earns each week.  Which linear function below best models the relationship between the amount of money the waitress earns(M) and the amount of tips(t) she receives?  How much money would she earn in a week if she receives $252 in tips?

• M = 0.75t + 100 and $289

• M = 0.75t + 100 and $189

• M = 75t + 100 and $289

• M = 100t + 75 and $25,275

In the equation, y = mx + b, the letter b is the ___________.

• y-intercept

• x-intercept

• slope

• rate of change

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

• -3

• 3

• 4

• -4