y = mx + b
y = -1/3x + 5
slope-intercept form
y – y1 = m(x- x1)
m -> slope, (x, y)->coordinates of the point
slope
steepness, comparing staircases
5feet, 10feet
slope = 5/5 = 1, 10 /5 = 2, 50/15 = 10/3
slope is vertical change/horizontal change = rize / run
positive slope is uphill, negative slope is downhill
y = mx + b
m is always the slope
b is the y-value of the y-intercept
y = 3x – 7
slope:3
y-intercept:(0, -7)
Introducting to Graphing
charged $10 per hour to rake leaves
5hour $50
10hour $100
x hour $10x
graphing is order pair
x-intercept(3,0)
y-intercept(0, -2)
horizontal line and vertical line
(2, 0),(2, 3),(2, -3)
x=2
-> x=3
Linear equation
properties of linear equations
x + 3 = 4
5(x+10)-30 = 5x – 18
equation is false means “Contradiction”, no solution.
pythagorean theorem
4^2 = 16
x^2 = 25, x = 5
√64 = 8
√1 = 1
right triangle 90°
a^2 + b^2 = c^2
hypotenuse 6, 8, 10
Algebraic expressions
A variable is: A symbol or letter that can be used to represent an unknown value
coffee …$2.00
tea …$3.50
Juice …$1.25
4 coffees and two teas calculate
4c + 2t = $15.00
3x + 2 cannot be determined
evaluate: find a value for an expression by substituting a value in for your variable
when x = -2, 3x + 2 = -4
care order of operation
7 + 3(x-2) when x=4
Decimals and Percents
If you have 1/2 of a candy bar, what percent of the original candy bar do you have left?
50%
cent mean 100 in franch, 100% = 1
$40, sales tax 6.75%, tax is $2.7
unit conversion
the world’s most amazing number!
1) multiplication
2) division
3/3 = π/π = -4/-4 = 1
12 eggs = 1 carton
12 eggs / 1 carton = 1
conversion factor: a number that relates amount of one thing to amount of another.
cartons -> eggs 12eggs = 1carton
yards -> feet 3feet = 1yard
liters -> ounces
dollar -> Euros
1 mile = 5280 feet
1 gallon = 4 quarts
1 gram = 1000 milligrams
1 pound = 16 ounces
1 mile = 1.609 Km
if you run 5 km, 3.1 miles you run
1 mile = 1760 yards
1 yard = 3 feet
1 m = 1.093 yards
1 km = 1000m
1 m = 100cm
1m = 1000mm
1gal = 16cups
1 gal = 3.785liters
Ratios
Rates: compare two quantities with different units
Ratios: compare two quantities with the same units
ex. “three out of five dentists recommend toothtaste.”
1/2 exact same meaning 1:2
3/5 -> 3:5
8/10 -> 4:5
200/500 -> 2:5
2/9 -> 2:9
Rates
learning the ratio and rates is super important
35 MPH(unit)
-> 35 miles per hour
35 miles / 1 hour
example
$12 / 1hour, 4,000,000babies/1year, 260calories/20 ounces of coke
150 miles / 3 hours = 50 miles / 1 hour -> unit rate
50 miles per hour
A unit rate is any rate where the value of the denominator is 1
pretzelicious: $3.50, 15ounces -> $0.23/ounce
pretztastic: $3.6, 18ounce -> 0.20/ounce
Scientific Notation
US National Deficit: 17 trillion dollars
$17,000,000,000
1.7 * 10^10
10^4 = 10,000
15,000:standard notation
1.5 * 10^4:scientific notation
negative powers
1.5 * 10^-4 = 0.00015
3.2* 10^-5 = 0.000032
2,700,000,000 -> 2.7 * 10^9
convert to scientific notation
34,000,000 -> 3.4 * 10^7