Question

Is \[ - 4x + y = 0\] a direct variation and if so, how do you find the constant?

Answer 1

Hint: Here The question is related to the graph. But here we are not plotting the graph. Here we check if the value of “y” depends directly on the value of “x”. First we have to arrange the equation for the graph and hence we obtain the required result for the given question.

Complete step-by-step answer:
A graph of a function is a set of ordered pairs and it is represented as \[y = f(x)\] , where x and f(x) are real numbers. These pairs are in the form of cartesian form and the graph is the two-dimensional graph.
Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If b is directly proportional to a the equation is of the form \[b = ka\] .
Usually it is represented as \[y = kx\] and k is the constant of variation.
Now consider the given question
 \[ - 4x + y = 0\]
Take y to the RHS, while shifting the term the sign of the term will change
 \[ \Rightarrow - 4x = - y\]
Cancel the negative sign on the both sides and we get
 \[ \Rightarrow y = 4x\]
Hence the equation is a direct variation. The constant of variation for this equation is 4.
So, the correct answer is “4”.

Note: The word direct variation means the variation will be applied or implied directly to the equation of the graph. Here we need not to plot the graph for this equation. Here we find only the constant of variation. where the coefficient of x.