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A "direct variation" between x and y means the equation is of the form: y = kx where "k" is some number. In order for the point (6, 2) to be on this line, its coordinates must fit this equation. So: 2 = k*6 Dividing both sides of this by 6 we get: So we know that the "k" for this equation must be 1/3. That makes the equation:
Answer: The graph that represent direct variation in the attached figure. Step-by-step explanation: A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or. In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes ...
If the graph is a straight line passing through the origin (0,0) with a slope of 3, then the function can be described as 'direct variation; k=3'. On the other hand, in an inverse variation , as x increases, y decreases, and as x decreases, y increases.
The general form of 'Direct Variation' is y = kx, where k is a constant i.e. it does not have a y-intercept. Now, according to our options, we see that the figures of A,B,C are the graphs of the straight lines given by y =-2x+2 , y=2x+2, y=-2x+2 respectively.
The same is true for Graph Two and Graph Three. Graph Four shows a direct variation, but its graph is not a straight line; therefore, it is not a direct variation. Graph Five is the only straight line that passes through the origin, which means it is a direct variation. Thus, the correct answer to this question is C. Graph Five.
The graph represents a direct variation. How to determine the type of graph. From the graph, we have the following ordered pairs (x,y) = (0,0), (2,4) and (3,9) Rewrite as: (x,x^2) = (0,0^2), (2,2^2) and (3,3^2) The above means that, the equation of the graph is: i.e. y varies directly to the square of x. Where the proportionality constant is 1 ...
The graph has a constant of variation of 3, so it represents a direct variation. The graph has a slope of 3, so it represents a direct variation. The graph has a positive slope, so it does not represent a direct variation. The graph does not begin at the origin, so it does not represent a direct variation.
The graph has a constant of variation of 3, so it represents a direct variation, which is correct Option (A). What is direct Variation? Direct Variation is defined as proportionality relationship in which two quantities when a quantity increases and the other quantity also increases , then those two quantities are called to be in direct variation .
The linear function showing direct variation is represented by Graph D, as it is the only graph where the line passes through the origin (0, 0) and has a consistent rate of change. To determine which linear function shows a direct variation, we need to identify the function with a line passing through the origin (0,0), which means that the y ...
Graph D On a coordinate plane, a line goes through points (0, 0) and (1, negative 2). Graph A Graph B Graph C Graph DWhich linear function shows a direct variation? Graph A On a coordinate plane, a line goes through points (negative 1, 0) and (0, 2). Graph B On a coordinate plane, a line goes through points (0, negative 2) and (0, 1).