Properties
What Property say that a + b = b+ c
Commutative Property of Addition
Solve for x:
x + 12 = 3
x = -9
What is the distance formula?
d = rt
The slope of a line = _____ over ______
Rise over run
Graph the equation y = 2
horizontal line
What property says that a(b + c) = ab + bc
distributive property
What do you need to do to 8x + 2 to get x by itself?
-2, divide by 8
write the distance formula in terms of r and in terms of t.
r = d/t t = d/r
y = ax + b is what form?
slope-intercept form
Graph the equation x = 4
vertical line
Show an example of the associative property of addition and multiplication - 2 separate examples
(a + b) + c = a + (b + c)
a(bc) = (ab)c
Solve for x, give you answer in decimal form:
-5x +8 = -7
x = -1/5 = -0.2
Daisy swam from the shore to an island and back. On the way there she swam against the current at 5 miles per hour. On the way back she swam with the current at 7 miles per hour. The swim took her a total of 3 hours. Let x represent the time she spent swimming against the current. Draw a diagram accurately showing this information.
What are the x and y intercepts of the following equation?
2x - 6y = - 12
x = -6
y = 2
Graph the lines y = 3x + 2
y = 3x - 2
y = 3x
Make two observations about these lines and their equations.
parallel - their slopes are the same
Use the commutative property of multiplication to rewrite 4(a + b)
(a + b)4
Solve for x:
7x - 5 = 4x + 13
x = 6
Daisy swam from the shore to an island and back. On the way there she swam against the current at 5 miles per hour. On the way back she swam with the current at 7 miles per hour. The swim took her a total of 3 hours. Let x represent the time she spent swimming against the current. Use the diagram you drew earlier to write and equation with the two expressions.
5x = 7(3 - x)
5x = 21 - 7x
Graph the following equation by first putting it in slope-intercept form. y - 2x = 5
x = -6
y = 2
How many weeks are there in a year?
52
Use the distributive property to rewrite 4(2y +22)
8y + 88
solve for x:
5(x + 6) = 8(x - 3)
18
Daisy swam from the shore to an island and back. On the way there she swam against the current at 5 miles per hour. On the way back she swam with the current at 7 miles per hour. The swim took her a total of 3 hours. Let x represent the time she spent swimming against the current. Use the equation to find out how far it is from the shore to the island.
x = 1.75 h 5(1.75) = 8.75 mi
What are the slope and y-intercept of the equation 5y = 3x +5
slope = 3/5
y-intercept = 1
On two separate graphs graph the following pairs of equations:
Graph 1: y = 3x - 4 and y = -1/3x +1
Graph 2: y = -2x +3 and y = 1/2x + 5
What do you notice about the relationship between the lines and the slope?
Perpendicular lines have the opposite inverse slopes.