Distributive Property
7(x + 4)
7x + 28
3/5x - 1/4x
7/20x
How many solutions are there?
5(x - 2) = 8x + 3(2 - x) - 8
Infinite Many Solutions
Myron is filling an empty teapot with water. The water fills the teapot at a rate of 4 fluid ounces per second. Write an equation to show how the amount of water in the teapot changes over time.
y = 4x
Using the slope formula, find the slope of the line through the points (0,0) and (3,12).
4
1/2(x + 2)
1/2x + 1
-0.57x + 0.27x
-0.3x
How many Solutions?
9(t - 4) = 3t - 20 + 6t + 16
no solution
An artist makes green paint by mixing 1 ounce of blue paint for every 3 ounces of yellow paint. Write an equation to represent the situation.
y = 1/3x
Using the slope formula, find the slope of the line through the points (-3,1) and (1,-3).
-1
-6(x - 6)
-6x + 36
-5/6x - 7/30x + 1/5x
26/30x = 13/15x
five times x plus twelve equals thirteen times x minus four
one solution
For an annual membership fee of $300, Mr. Bailey can join a country club that would allow him to play a round of golf for $25. Without the membership, the country club charges $75 for each round of golf. How many rounds of golf would Mr. Bailey have to play for the cost to be the same with and without a membership?
300 + 25x = 75x
(-2, 10), (-1, 7.5), (0, 5), (1, 2.5), (2, 0)
What is the slope of this line?
20(x + 1/2)
20x + 10
35 - (2c + 3)
32 - 2c
How Many Solutions?
30x + 930x - 14 = 24(40x + 67)
No solution
A line passes through the point (2,10) and has a y-intercept of 4. What is the equation of the line?
y = 1/3x + 4
Colton is heating a pot of water. He records the temperature of the water in the pot every minute. This equation models Colton’s data, where x represents the number of minutes the water has been heated, and y represents the temperature of the water in degrees Fahrenheit.
y = 7.5x + 40
What does the coefficient 7.5 in the equation represent in the context of this situation?
The coefficient 7.5 in the equation represents the slope which is the how much the temperature of the water in the pot goes up every minute.
-1/2(x - 2/3)
-1/2x + 2/6 OR -1/2x + 1/3
6(x - 6) + 8
6x -28
How Many Solutions?
3(4x + 2) = 16x + 4 - 4x + 2
infinitely many solutions
Ling bought a bicycle on sale for 30% off the original price, for $86. What was the price of the bicycle before the sale?
86 = p - .30p
OR 86 = .70p
What is the slope in this linear relationship?
(-2, 1), (-1, 3), (0, 5), (1, 7)
The slope of the line is 2