A rental agency rents their equipment for $12 per hour and requires a flat fee of $25. Write a linear model that shows the cost, y in terms of hours rented, x.
A pump removes 1000 gal of water from a pool at a constant rate of 50 gal/min.
a. Write an equation to find the amount of water y in the pool after t minutes.
b. Graph the equation and interpret the t- and y-intercepts.
Jacksonville, Florida has an elevation of 12 ft above sea level. A hot-air balloon taking off from Jacksonville rises 50 ft/min. Write an equation to model the balloon’s elevation as a function of time. Graph the equation. Interpret the intercept at which the graph intersects the y-axis.
elevation = rate * time + starting elevation
Let y = the balloon’s elevation.
Let x =time (in minutes) since lift off.
An equation:
The y-intercept is:
It represents:
A tree 5 ft tall grows an average of 8 in. each year. Write and graph an equationto model the tree’s height h after x years. Make sure that the units are the same (in or ft,but not both units)
The marching band holds a fund raiser each year in which they sell t-shirts and sweatshirts. T-shirts cost $7 while sweatshirts cost $15. The band needs to raise $3000. Write a model to show the number of t-shirts and sweatshirts they need to sell to reach their goal?
The base pay of a water delivery person is $210 per week. He also earns 20% commission.
Find slope, what does it represent?
Find the y-intercept, what does it represent?
Write a linear model to show earnings after x amount of sales.
You are sent to the store to buy sliced meat for a party. Roast beef cost $4.29/lb and Turkey cost $3.99/lb. Write an equation to relate the pounds of each you could buy with $30.
x = lbs of Roast Beef
y = lbs of Turkey
Write an equation in standard form to find the minutes someone who weighs 150 lbs would need to bicycle and swim laps in order to burn 300 calories.
x = Minutes Bicycling
y = Minutes Swimming
The grocery store sells kumquats for $3.50 a pound and Asian pears for $1.75 a pound. Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $24.
SUMMARY
Equations of Lines
Slope-Intercept Form / Standard FormY = mx + b / Ax + By = C
One-Variable Changing / Two Variables Changing
Science A candle is 6 in. tall after burning for 1 h. After 3 h, it is 5.5in. tall. Write alinear equation to model the height y of the candle after burning x hours. When will the candle be 4 in. tall?
Step 1:Identify the data points: (1, 6)
and (3, 5.5) as (x1, y1) and (x2, y2).
Step 2:Write the equation of the line.
Find slope and use point slope form OR
Put points in calculator and use LinReg
Step 3:Use your model to evaluate when the candle will be 4in tall (height is y)
An empty 5-gal water jug weighs 0.75 lb. With 3 cups of water inside, the jugweighs 2.25 lb. Predict the weight of the jug with 5 cups of water inside.
There are 55 blades of grass in 1 in.2 of lawn. There are 230 blades of grass in4 in.2 of the same lawn. How many blades of grass are in 3 in.2 of lawn?
A 2-mi cab ride costs $5.25. A 5-mi cab ride costs $10.50. Let m represent the number of miles and c represent the cost. Write the equation to model cost of the cab write. What is the independent variable? What is the dependent variable? How much does a 3.8-mi cab ride cost?
2.4 Linear ModelsPage 1 of 13