Graphing a Direct Variation Using a Table of Values

A direct variation can be represented graphically by a line that passes through the origin on a coordinate plane. A table of values can help get the line of a direct variation given in the form y=kx. Consider, for example, the following equation of a direct variation. y=3x Three steps can be followed to draw the line for this equation.

Write the Equation in the form y=kx

Recall that a direct variation equation can be written in the following forms. y=kx, y/x=k, or y/k=x If a direct variation equation is in the form of yx=k or yk=x, then rewrite it to be in the form of y=kx. This form will help to apply the next steps more straightforwardly.

y/x=k

MultEqn

LHS * x=RHS* x

y=kx

Note that the given equation is already in the form y=kx where the constant of variation k is 3.

Make a Table of Values

A table of values can be made by substituting several random values for x and then solving the equation for y.

x	y=3x	y	(x,y)
-1	y=3( -1)	-3	( -1, -3)
0	y=3( 0)	0	( 0, 0)
1	y=3( 1)	3	( 1, 3)
2	y=3( 2)	6	( 2, 6)
3	y=3( 3)	9	( 3, 9)

Plot the Ordered Pairs and Graph the Line

Finally, plot the ordered pairs from the table of values and connect them with a straight line.

It is worth to keep in mind that if a line does not pass through the origin then it does not represent a direct variation. In other words, there is not a proportional relationship between the variables x and y.

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