- How do you find the independent and dependent variable?

- What is the direct variation formula?

- How do you write a direct variation equation?

Hours Worked

Money Earned

Drew gets paid hourly at his job. If Drew gets $50 dollars for a $5.00 hour shift, how much will he be paid for a $7.00 hour shift? Find K and write an equation to solve this question. This question is actually asking us to find K which is the direct variation formula

Notice with direct variation as,

x increases, y also increases.

Today we are going to talk about direct variation, and here is an example of what we are looking at. When Y varies directly with X that’s a direct variation. So here’s our example. If Y is ten when X is is five what is K Well first of all we need to see a set formula. So here are the rules for direct variation. The formula for solving for a direct variation is Y=KX. This is the direct variation formula Y equals K times X and I always think it is the same as Y equals MX plus B but B is gone, it is zero M and K are very similar they are kind of like slope, then we will solve for K by plugging in our X and Y values and with direct variation we are going to end up dividing y by x and then you take the K and plug it back into the formula .You will have your generic Y, just leave the variable there, your K and then your generic X Let’s work through this example to see how it works. We will write the formula down. Y equals KX and when Y is ten X is five. So I will plug in ten for Y and five for X to solve for K notice the rules I’m just going to divide both sides by five and I get two is equal to K so that’s my first step I have to solve it for K Now let’s go back and take our K and plug it into our formula. Remember it is Y equals KX and to write the equation all I do is replace K with our 2 so our equation would be Y equals 2X and we are done.

"k" equals the constant of proportionality.

"y "equals your y coordinate. You may also think of y as the **dependent variable** in science because it depends on x, and varies according to "x".

"x" equals your x coordinate. You may also think of x as the **independent variable** because it can be manipulated or changed.

If you work 40 hours in a week and make $800. How much will you make if you work 60 hours?

You will use y=kx because it is a direct variation. As the hours worked increases so does your paycheck.

Amount of paycheck =y

Number of hours worked= x

y/x =k ( which is your constant)

The amount of paycheck/Number of hours worked =K

Step 1 800= K40

Step 2 20=k

Step 3 Plug K into the formula y = 60*20

Step 4 y=$1200

If y varies directly as x, and y = 10 when x = 5, find k and write an equation that expresses this variation

Step 1 10=5*K

Step2 Divide both sides by 5 10/5=5/5*K

Step 3 K= 2

Step 4 The equation would be y = 2x

Aaron earns $48 for a 6 hour shift at Moe’s. The amount of money he earns varies directly to the number of hours worked.

Find the constant, k, and find the amount of money he will earn Saturday for a 10 hour shift.

Direct variation is defined as a mathematical relationship between two variables whose ratio is a constant. In other words, the two variables change in the same direction. If one variable increases, the other variable increases, if one decreases so does the other variable.