A. Tell whether x and y show direct variation. Explain your reasoning.
1. x = y - 2 / 9
2. 5x - 3y = 0
My answer: Yes because 5 and 3 pass through the origin (0).
1. no, I see a constant
2. yes, which you had
but your "reasoning" statement makes no sense
did you mean to say, "because (0,0) satisfies the equation?
To determine whether x and y show direct variation, we need to examine the equations given and see if they can be written in the form y = kx, where k is a constant.
1. x = (y - 2) / 9
To check if this equation represents direct variation, let's rearrange it to the form y = kx:
Multiply both sides of the equation by 9:
9x = y - 2
Add 2 to both sides of the equation:
9x + 2 = y
Now our equation is in the form y = kx, where k = 9.
Therefore, x and y show direct variation because y can be expressed as a multiple of x.
2. 5x - 3y = 0
To check if this equation represents direct variation, let's rearrange it to the form y = kx:
Add 3y to both sides of the equation:
5x = 3y
Divide both sides of the equation by 3:
(5/3)x = y
The equation can be written as y = (5/3)x, where k = 5/3.
Therefore, x and y show direct variation because y can be expressed as a multiple of x.
So, both equations given show direct variation, as y can be expressed as a multiple of x in both cases.
To determine if two variables, x and y, show direct variation, you need to check if there is a constant ratio between them. In other words, if you divide one variable by the other and it always gives you the same value, then they show direct variation.
Let's analyze the two equations given:
1. x = (y - 2) / 9
In this equation, x is expressed in terms of y. To check if x and y show direct variation, we can rewrite the equation as:
9x = y - 2
Now, let's check if there is a constant ratio between x and y. We can rearrange the equation to isolate y:
y = 9x + 2
Now, we can see that the coefficient of x is 9, which means for every unit increase in x, y increases by 9. Therefore, x and y do not show direct variation.
2. 5x - 3y = 0
To determine if x and y show direct variation in this equation, we can rearrange it to solve for y:
3y = 5x
y = (5/3)x
Now, we can see that the coefficient of x is 5/3. This means that for every unit increase in x, y increases by 5/3. Therefore, x and y show direct variation.
Your answer is correct. In equation 2, x and y do exhibit direct variation since the ratio between them is constant (5/3).