Proportional Equations
Describe what an equation that represents a proportional relationship looks like.
y = ___x y = kx y = mx
What is the ratio of the following relationship and is it proportional? For one sandwich is cost $5.75, for 3 it cost $17.25, and for 6 it cost $34.50.
5.75:1
Yes
Two quantities are __________ if they have a constant ratio between them.
Proportional
Navelle earns $12 per hour. Write an equation that represents Navelle's earnings.
y = 12x
Every 2.5 hours, a machine produces
2250 basketballs. What is the unit rate of this proportional relationship?
900 basketballs per hour
Is y = 8x + 2 proportional?
No
What is the ratio of the following proportional relationship? AND What is the Constant of Proportionality? The amount of money earned for 2 hours is $15.00 and for 3 hours is $22.50.
7.5:1
k = 7.5
A ratio that compares two quantities with different kinds of units is called a __________.
rate
Gianna reads 27 pages in 9 minutes. At What rate does Gianna read?
y = 3x
How do you know a graph is proportional?
It goes through the origin and it is a straight line
Jake is selling boxes candy bars to raise money for his baseball team. He makes $6 for each box of candy bars he sells. Write an equation to represent the situation. AND How much would Jake make if he sold 17 boxes?
y = 6x
$102.00
June has $120.00 in her checking account and she makes a $50.00 deposit in it each week. How much would she have in her account after making a deposit for 3 weeks? AND Is the relationship proportional? Give at least one reason.
$270.00 No. The ratios are not constant. The graph would not start at 0. The equation would not be in y = __x form.
When two related quantities do not have a constant ratio.
Non-proportional
Maxine works at law office. the equation y = 135x represents her earnings.Determine how much money she makes if she works 40 hours.
Maxine earns $5,400 in 40 hours.
y = 3x or y = 3x +2
y = 3x
Rachel's family of 4 went to the zoo and it cost them $52.00 for admittance. What is the Constant of Proportionality? AND What does it represent?
13 The cost of admittance for one person.
It costs $8.97 for 3 packages of turkey, $17.93 for 6 packages, and $26.91 for 9 packages. Is the relationship proportional? If yes, what is the constant of proportionality?
Yes 2.99
When a rate is simplified so it has a denominator of 1 unit. y/x
Unit Rate
The equation y = 55x represents the rate of the Long Island highway speed limit, in miles per hour. Let x represent the number of hours driven and y represent the total miles driven.
How long was Francis driving if he drove 247. 5 miles at the speed limit.
Francis drove for 4.5 hours.
Is this proportional: Jenny went to the store to buy groceries, no matter what she bought she would have to pay $1 to charity.
No +1
George and Lucy rode the bus and it cost them $11.78. Write an equation to represent this situation. AND How much would it cost for 5 people to ride the bus?
y = 5.89x
$29.45
How can you tell immediately that an equation is NOT proportional?
It has addition or subtraction
What is the Constant of Proportionality
If two quantities are proportional. The constant ratio between them is the CoP as a whole number with no labels.
If Jackson ate hamburgers at a rate of 3.5 hamburgers per minute and Jacen ate hamburgers at a rate of 4.7 hamburgers per minute, write an equation that could represent how many more hamburgers Jacen can eat more than Jackson.
y = 1.2x
A car went to the drive in and had to pay $5 per person and $4 for the vehicle. Write the equation.
y = total cost
x = people in the car
y = 5x + 4