Is every linear relationship a direct variation? Explain, please.
Answer (3)
direct variation: y=kx where k is some number thats not 0
that means if x is 2, y is 2k. if x is 1, y is k. if x is 0, y is 0.
notice: no matter what k is, when you put 0 in for x, y will always be 0. that means that a direct variation always goes through the origin, a.k.a. (0,0).
do all lines go through the origin? nah. a line is y=mx+b, where m and b are some numbers. a line is only a direct variation if b is 0. this makes sense because if b is 0, then the y-intercept is 0, so the line goes through the origin.
in conclusion, ****no, not all linear relationships are direct varations, but all direct variations are linear relationships.
A linear relationship is a relationship between two variables that can be represented by a straight line graph. A direct variation is a specific type of linear relationship where the ratio between the two variables remains constant. In other words, every direct variation is a linear relationship, but not every linear relationship is a direct variation.
An example of a direct variation is the equation y = kx, where k is a constant. The variable y is directly proportional to x, and the ratio y/x is always equal to the constant k.
On the other hand, a linear relationship that is not a direct variation can have a non-constant ratio between the two variables. One example is the equation y = mx + b, where m is the slope and b is the y-intercept. This equation represents a linear relationship, but the ratio y/x is not constant.
Not every linear relationship is a direct variation. A direct variation maintains a constant ratio between two variables and is expressed as y = k x , while a general linear relationship can have a constant added, like y = m x + b . Therefore, all direct variations are linear, but not every linear relationship qualifies as a direct variation.
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