Slope Formula
(0,0) and (4,3)
3-0/4-0
Slope = 3/4
A line going down from left to right has what type of slope?
Negative
Every 4 hours of work, Jesse earns $80. What is the unit rate?
Unit rate: 20
$20 per 1 hour of work
What is the unit rate/slope/constant of proportionality?
x y
1 10
2 20
3 30
4 40
Change in y/change in x
y= +10
x= +1
Slope = 10
What is the m in y=mx
Slope
(-16,5) and (0,13)
13-5/0--16
8/16
Slope = 1/2
To find the slope of a graph, I should first ____ then ____.
Rise then Run
True or false: In a proportional relationship, the constant of proportionality is NOT the same as the slope or unit rate.
False!
It is the same
What is the unit rate/slope/constant of proportionality?
x y
0 0
12 60
18 90
24 120
30 150
36 180
Change in x = +6
30/6=5
Slope = 5
Write an equation for the table:
x y
2 100
4 200
6 300
8 400
y=50x
50 is the slope
Whatever number you have for x, just multiply by 50 to get y.
(-2,-4) and (2,4)
4--4/2--2
4+4/2+2
8/4
Slope = 2
On a graph you rise 6 and run 3, what is the slope?
2
How can you tell if a graph is proportional/constant?
It is a straight line
Is the table proportional? Why or why not?
x y
0 0
3 6
5 8
7 10
Not proportional, different rate of change.
You cannot multiply the same number each time by x to get y.
A robot in a factor can create 350 shirts in 7 hours. What is the unit rate?
350/7
50 shirts in 1 hour (always simplify!)
(-1,2) and (0,-4)
-4-2/0--1
-6/1
Slope = -6
A graph has a point at the origin and (6,8) what is the slope?
Rise - 8, Run - 6
8/6, simplified 4/3
True or false: A proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant.
True
Find the slope:
x y
-12 -16
6 8
Change in y = 24
Change in x = 18
24/18
Slope = 4/3
Joe makes $115 in 2.5 hours at his current job. A new job offered him $180 for 4.5 hours of work. He wants to make the most money possible. Should Joe accept the offer from the new job or keep his current job? Explain.
He should keep his current job because he is currently making $46 per hour and the new job is only offering him $40 per hour. $46 hourly is more than $40 hourly.
(-2,-1) and (-3,0)
0--1/-3--2
0+1/-3+2
1/-1
Slope = -1
If a graph goes through the origin, (2,3) and (4,6), is it proportional?
Yes, constant unit rate/slope.
y=5x is the percent increase of a students grade per week. How many weeks would it take for the student to go from a 60% to a 90% in math class?
6 weeks
30% increase
5% per week
30/5=6
Fill in the missing number in the table:
x y
2 30
4 ___
__ 90
8 120
4:60
6:90
The equation y=25x represents the scenario where a car is traveled 25 miles in 1 hour. How long would it take for the car to travel 100 miles?
4 hours