Proportionality
What does proportional mean?
Equal Ratios or equal fractions - constant rate of change
What is unit rate and what operation do we use to get unit rate?
The rate for 1 of something, and we use division
What's the slope?
(0, 5) and (4, 17)
3 or 3/1
Which is slope?
y = mx + b
m is slope
What does a whole number with a negative exponent represent?
It would represent a fraction
Which is a proportional relationship?
A) Victor has a flat rate of $100 for his babysitting company then a $10 charge each hour.
B) Morgan gets paid $14 an hour as a paramedic.
B
Michael drives 650 miles in ten hours. What is his unit rate (if he drove the same speed for all ten hours)?
65 miles per hour
What is the equation for finding the slope of two points?
y2 - y1/ x2 - x1
y = 6x + 12
What's the slope?
6 or 6/1
If I was looking at a graph and I wanted to find the slope, what equation would I use?
rise/run or y/x
change in y/change in x
Hannah spends 3 hours a night on homework.
What's the equation?
y = 3x
I got paid $320 this week by working 40 hours! How much do I get paid per hour?
$8 per hour
In the equation y2 - y1/ x2 - x1, what do the little numbers mean?
Which coordinate pair is being used. It shows us that our second coordinate pair that is given to us will be first.
What's the slope?
y = 3/4x + 2
3/4
Solve 3x - 4 = -5 for x
-1/3
Give me a word problem that relates to this equation: y = 10x
Ex. Jill gets paid $10 per hour
This week I ate 10,500 calories. How many calories did I eat per day?
1,500 calories
Find slope: (2, 3) and (3, -4)
-7/1 or -7
Why would you not change an improper fraction into a mixed number when it comes to slope?
The numerator is telling you how far you are going up or down, the denominator is telling you how far you are going left to right. They are directions!
What is the slope in y=6x?
6
What is m?
m stands for the slope
Your teacher goes to get coffee every morning and buys herself and a friend a cup of coffee. If she goes to Starbucks, she pays $7. If she goes to Dunkin Donuts, she pays $6.75. What is the unit rate for the price of coffee at EACH place?
Starbucks: $3.50
Dunkin: $3.38
Find slope: (4, 19) and (5, 15)
-4/1 or -4
What equation do I use for a proportional relationship
y = mx
it's the same as y = mx + b, but b is the y intercept and it crosses through the y axis at 0, so the b is 0 and we don't need to write it.
From a table, you need to find the ____ _____ of _____ to find the slope.
Constant Rate of Change