Linear Change
If a linear relationship occurs between two variables, then the average rate of change is
constant
what are the two different forms of a line
Slope intercept and point slope
create a model of the distance, D, a driver is from Chicago if they are heading towards the city at 58 miles per hour and started 256 miles away?
D = 256 - 58t
Water is entering a storage tank at a constant rate of 235 gallons per hour. After 3 hours, the tank holds 1,961 gallons. How many gallons will the storage tank hold after 8 hours?
3136 gallons
How do you find the perpendicular slope of a line
Take the negative reciprocal
ie. Flip and Negate
The cost, C, of producing x-bikes is given by C = 22x + 132 . The revenue gained from selling x-bikes is given by R = 350x . If the profit, P, is defined as P=R-C, then create an equation for P in terms of x?
P = 328x-132
A computer is downloading files at a constant rate of 2.3 gigabytes per minute. After 15 minutes, 54.5 gigabytes have been downloaded. How many gigabytes will be downloaded after 40 minutes?
112
What is the perpendicular slope of the following line
y=-2/5x+9
What is
5/2
A school is making decals to sell as a fundraiser. The company they are purchasing the decals from charges a $70 art setup fee plus $2 per decal made. Which equation models the relationship between ๐ก, the schoolโs total cost and ๐, the number of decals the school purchased?
๐ก = 70 + 2d
A water tank is being filled at a constant rate of 3.5 liters per minute. After 12 minutes, 61.5 liters are in the tank. How many liters will be in the tank after 30 minutes?
124.5
What is the equation of a line that is parallel to
๐ฆ = โ2๐ฅ + 3 and passes through the point (4,โ9)?
y = -2x -1
A club is ordering T-shirts to sell as a fundraiser. The company they are purchasing the T-shirts from charges a $45 screen setup fee plus $8 per T-shirt made. Which equation models the relationship between ๐, the clubโs total cost, and ๐ , the number of T-shirts the club purchased?
c = 45 + 8s
Maya starts a long-distance bike ride. After 6 minutes, her bike computer says sheโs covered 2.1 kilometers. After 18 minutes, sheโs ridden 6.3 kilometers.
At this rate, how far will Maya have traveled after 50 minutes?
17.5 km
The linear function ๐(๐ฅ) contains the points (โ4, 3) and (4, 1)
Determine the equation of the line for ๐(๐ฅ) in point-slope form.
Will the line pass through the point (16,โ2)?
What is
y-3=-1/4(x+4) or y-1=-1/4(x-4)
Yes it will pass through the line
A water tower has a leak. 12 minutes after the leak was noticed there were 964 gallons of water left in the tank and 60 minutes after the leak was noticed there were 868 gallons of water left in the tank. Write a linear equation that can be used to model this equation
y = -2x + 988