Slope-Intercept
A music app charges $2 to download the app plus $1.29 per song download. What is the rate of change (m) for this problem?
m = 1.29
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, $5,050 is collected. Write a linear equation to model this situation. (Double points if you can write the equation in slope-intercept form)
x = children, y = adults
1.50x + 4.00y = 5050
slope-intercept: y = -0.375x + 1262.5
Chit-Chat Wireless charges $0.30 per minute plus a monthly base fee. In September, Maggie used 120 minutes and her bill was $51. What is the rate of change for this problem?
m = 0.30
To serve 1 person at a local restaurant, it takes 10 minutes. To serve 5 people, it takes 18 minutes. Write an equation to model this situation. What is one point from this problem?
(1,10) or (5,18)
Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. What is the starting point (b) for this problem?
b = 35
A landscaping company ordered 17 plants and 8 trees for a total of $964. Write a linear equation to model this situation. (Double points if you can write it in slope-intercept form)
x = plants, y = trees
17x + 8y = 964
slope-intercept: y = -2.125x + 56.7
There is a daily fee for renting a moving truck, plus a charge of $0.50 per mile driven. If driven 48 miles, it costs $64 to rent a truck. What is the sample point (x,y) for this problem?
(48,64)
The cost for 7 dance lessons is $82. The cost for 11 lessons is $122. What are the two points for this problem?
(7,82) (11,122)
The late fee for library books is $2.00 plus 15 cents each day for a book that is late. Write a linear equation (y = mx + b) to model this situation
y = .15x + 2
A road side vegetable stand sells pumpkins for $5 each and tomatoes for $3 each. The total sales on a certain day was $98. Write an equation to model this situation (double points if you can write it in slope-intercept form)
x = pumpkins, y = tomatoes
5x + 3y = 98
slope-intercept : y = -1.67x + 19.6
To lease a new car, you must make a down payment when you sign the lease, then pay $199 per month. Six months after signing the lease, Mr. Scott had paid $2,694. Write an equation to model this situation. (Double points if you can write it in slope-intercept form)
y - 2694 = 199(x - 6)
slope-intercept : y = 199x +1500
To order tickets online to a hockey game, there is a processing fee plus the cost per ticket. The cost for 5 tickets is $174.45. The cost for 8 tickets is $271.95. What is the slope for this problem? (Hint: use slope formula!)
(5, 174.45) (8, 271.95)
m = 32.5
A group of mountain climbers begin an expedition with 250 pounds of food. They plan to eat a total of 12 pounds of food per day. Write a linear equation (y = mx + b) to model this situation.
y = -12x + 250
A tire dealer sells all-season tires for $68 each and all-terrain tires for $125 each. In one day, the sales for both tires totaled $3,926. If 14 all-terrain tires were sold, write and solve a linear equation to find the number of all-season tires sold.
x = all-season tires, y = all-terrain tires
68x + 125y = 3926
x = 32 tires
Since Beth was born, the population of her town has increased at a rate of 850 people per year. On Beth's 9th birthday, the population was nearly 307,650. Write and solve a linear equation to find the population on Beth's 16th birthday.
y - 307650 = 850(x - 9)
slope-intercept : y = 850 x + 300000
y = 313,600 people
An international calling plan charges a rate per minute plus a flat fee. A 10-minute call to France costs $3.19. A 15-minute call to France costs $4.29. What is the slope for this problem? (Hint: use slope formula!)
(10, 3.19) (15, 4.19)
m = 0.22
An airplane at 30,100 feet above the ground begins descending at the rate of 2,150 feet per minutes. Write and solve a linear equation to find how many minutes it will take the plane to reach the ground (0 feet).
y = -2150x + 30100
x = 14 mins
You re buying the hamburgers and chicken for a party. The hamburgers cost $2.75 per pound and the chicken is $3.50 per pound. If you have $75 to spend, write and solve a linear equation to find how many pounds of chicken you can afford if you buy 12 pounds of hamburger.
x = hamburgers, y = chicken
2.75x + 3.50y = 75
y = 12 pounds
A candlestick burns at a rate of 0.2 inches per hour. After 8 straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the total height of the candle.
y - 13.4 = 0.2(x - 8)
slope-intercept: y = -.2x + 15
y = 15
Jake spent a three-day weekend on the lake. On Saturday, he rented a pontoon boat for three hours and paid $435. On Sunday, he rented the same boat for five hours and it cost him $190 more than it did the day before. Write an equation to model this situation. (Double points if you can write it in slope-intercept form)
(3, 435) (5, 625)
y - 435 = 95(x - 3)
slope-intercept : y = 95x + 150
$1400 total