Direct Variation
Direct Variation relations always pass through what point on the Cartesian plane?
(0,0) aka the origin
True or False: Partial Variation does not have a constant rate of change
False
what is the equation for slope?
rise/run
A farmer plants 200 tomato seeds every 4 hours. What is the rate of change?
50 seeds per hour
complete the sentences:
y is always the _______________ variable
x is always the _______________ variable
y is always the dependent variable
x is always the independent variable
What is the equation of a line for a direct variation relation
y = ax
or
y=mx
What is the difference between Partial Variation and Direct Variation?
Direct Variation has a y-int of 0 and its equation is y=ax
Partial Variation has a y-int that does not equal 0 and its equation is y = ax +b
slope is represented by what variable in the equation of a line?
a
A car rental company charges a flat rate of $50 plus $20 per day for renting a car. Write an equation to represent this scenario
y = 20x+50
What is the most common example of an independent variable (as mentioned in class)
the passing of time (day, hours, seconds, minutes, etc.)
How would you write the equation of a line representing direct variation if π¦ is twice π₯?
y = 2x
Give 2 synonyms of "y-intercept"
Initial cost & Initial Value
Name 3 synonyms of slope
Rate of change, rise over run, constant of variation
A population of bacteria doubles every hour. Write an equation representing the population (π) as a function of time (π‘). If the initial population is 100 bacteria, predict the population after 6 hours.
y = 2x +100
112
a = 1/2
y = 1/2x + 2
If π¦ varies directly with π₯ and π¦=9 when π₯=3, what is the value of π¦ when π₯=8?
y = 24
Slope of 3
y=3x
What are 3 properties of graphs of partial variation?
- Does not pass through the origin
- Resembles a straight line
- Its equation is always in the form y=ax+b
- "b" represents the initial value and is always greater than 0
- "a" represents the slope
What is the slope of a vertical line? Why? - Explain using mathematical reasoning
undefined: it has a rise, but no run, meaning it is rise/0, since anything divided by 0 is not possible, the slope is undefined
What is the constant of variation in km/h if you travel 4km in 30 mins?
8 km/h
What is the equation of a line if it passes through the points (0,40) and (5, 15)
y = -5x+40
A company manufactures bikes, and the production cost per bike varies directly with the number of bikes produced. When 100 bikes are produced, the total production cost is $15,000. If the company produces 150 bikes, what will be the total production cost?
$22,500
If π¦ varies partly with π₯ and π¦=10 when π₯=2, and π¦=30 when π₯=12, what is the value of π¦ when π₯ = 15?
equation of the line: y = 2x + 6
when x =15, y = 36
Gym A offers a membership for 50$ a month with a joining fee of 10$. Gym B offers a membership of $40 a month with a $30 joining fee. After one year, which one allows you to save more and by how much?
Option A: y = 50x + 10
$610 in a year
Option B: y = 40x + 30
$510 in a year
Saving 100$ with option B
A company pays its employees a base salary of $2000 per month plus a commission of 5% of their total sales. Write an equation representing the total monthly earnings (πΈ) as a function of total sales (π₯)
y = 0.05x + 2000
What is the x-intercept of the equation y = 3x - 9
x-intercept at x = 3 or (3, 0)