Tell whether equation represents direct variation. If so, identify the constant of variation

1. Y=8x
Ans: yes, it represents direct variation because
its in the form Y=kx. Constant of variation: 8

2. Y=2x+1

3. 3x+y=6

Please help, not too sure if I am understanding this correctly. Completed first problem.

Let's analyze the second and third equations.

2. Y=2x+1:
This equation does not represent direct variation because it is not in the form Y=kx. In direct variation, the equation should have only one variable on the left side and a constant multiple of that variable on the right side.

3. 3x+y=6:
This equation also does not represent direct variation because it is not in the form Y=kx. In direct variation, the equation should have only one variable on the left side and a constant multiple of that variable on the right side.

Therefore, only the first equation, Y=8x, represents direct variation with a constant of variation equal to 8.

No problem! I'm here to help you. Let's go through each of the remaining problems together.

2. Y=2x+1:
To determine if this equation represents direct variation, we need to check if it is in the form Y = kx, where k is a constant. In this case, the equation is not in the form Y = kx because there is an additional "+1" term. Therefore, it does not represent direct variation.

3. 3x+y=6:
Similar to the previous equation, we need to check if it is in the form Y = kx. However, in this case, the equation is not in the form Y = kx because the given equation involves both x and y terms on the left-hand side, and a constant term on the right-hand side. Therefore, it does not represent direct variation.

I hope this clarifies things for you! If you have any more questions, feel free to ask.

First problem is correct.

A direct variation will have the y-intercept as zero, so it is in the form
y=kx, where k is a constant.
In other words, a direct variation is a straight line that passes through the origin.
Q2 and Q3 are not direct variations, because the y-intercepts are 1 and 6 respectively.

y=2x+1 yes 2x