Proportional Relationships
What equation do we use to represent proportional relationships?
y=kx
Simplify by combining like terms.
x2+3x2+2x+x+x+(-2)
4x2+4x+(-2) OR 4x2+4x-2
X2 + 2x - 1
Solve when x=3
14
Simplify using the distributive property.
2(7x+3)
14x+6
Jacob drinks 3 cups of water in 1/4 of a day. How many cups of water does Jacob drink in 4 days?
12 Cups
Josiah makes 30 dollars and hour cutting grass. What is the rate of change?
15
Simplify by combining like terms.
7-4x+(-1)+8x
4x+6
4x2 + 2x
Solve when X= 2
20
14x-28
7(2x-4)
Jenna Runs 1/3 of a mile in 2 minutes. How long does it take her to run a mile?
6 Minutes
What two things have to be true for a graph to be proportional?
Simplify by combining like terms.
-3 - 2x + (-1) + 4x
2x + (-2) OR 2x-2
-2x2 + 4x + 5
Solve when X=6
-43
Simplify using the Distribute Property.
4(5x-3) + 8
20x-4
The Jenkins family drinks 3/4 of a gallon of orange juice every 3 days. How much orange juice do they drink per day?
3/12 or 1/4
y=2.5x
Create a table with the x values being 0, 2, 4 and 6
0, 5, 10, 15
-3 + 4x + 2 - x + (-7) + (-2x)
x + (-8) OR x -8
-7x - (-5)
Solve when x=3
-16
Factor.
18x + 27
9(2x+3)
A car travels 75 miles per hour. At this rate, how many miles does the car travel in one minute?
1.25 miles.
Ian's swimming lessons cost $400 for 5 days. Write an equation to represent this relationship, where x is days and y is cost.
y=80x
-3 - 4x + 5 +(-3) - (-2x) - x
-3x + (-1) OR -3x - 1
4x + (-3) + 5 - x
Solve when x=4
Simplify using the Distributive Property.
-3(2x-3)
-6x+9
Joan’s Candy Emporium is having a sale. 5 pounds of gummy bunnies are selling for $8.
How much will two pounds cost?
What is the unit rate for gummy bunnies?
b. 1 pound for $1.60